Lurking down a side street, in the tangled maze of lanes and railway viaducts south of the River Thames, stands one of the strangest new sights in the capital. Look up on the corner of Union Street and O’Meara Street, and you will see a white brick building with a great furrow gouged out of its facade, as if it’s been attacked with a gigantic ice cream scoop. It is a true architectural WTF moment that has been stopping passersby in their tracks since the scaffolding came down a few weeks ago.

Follow the direction of the two-storey gouge, and observant onlookers will find that it precisely frames the shape of the rose window of the church next door, making it look a bit like the building might have been melted by holy rays emanating from the stained glass: a facade sculpted by the power of the Lord?

“We wanted to respect our neighbour,” says Jonny Plant, architect of this curious new concave office building. “The church had always been overlooked, tucked down the side street next to the railway viaduct, so we wanted to celebrate it and draw people’s attention to it.”

His firm, Lipton Plant (since merged with Corstorphine & Wright), had been commissioned to expand the four-storey redbrick building on the corner with an infill extension to the side, and an extra storey on the roof. The building’s ground floor had always filled the entire footprint of the site, but the upper floors had been recessed back from the street, to politely align with the facade of the Roman Catholic church – a grade-II listed romanesque structure, built in 1892 by prolific church architect Frederick Walters.

“The developer originally wanted to fill the whole site and bring the building right up to the street edge,” says Father Christopher Pearson, priest of the Church of Most Precious Blood. “But we had just spent a lot of money restoring the church, and we didn’t want to be hidden. They were very accommodating and listened to our concerns – and we are tickled pink with the result. It’s as if the building is saying saying: ‘Ta-daa! Here we are!’”

There is a reason that the church had always been somewhat secluded. For over 200 years after the Act of Uniformity in 1559, outward observance of the Roman Catholic faith was illegal in England. Even after the Catholic emancipation in 1829, and further relaxation of the laws in 1850, Catholic churches were often squirrelled away down side streets and set back from the road. Over 130 years after its completion, Most Precious Blood is now more visible than ever, theatrically framed by a most precious viewing cone.

History is awash with “spite buildings”, architectural monuments to neighbourly grudges, designed to block views and obstruct daylight. But this is the opposite: a surreal love-thy-neighbour tribute wrought in glazed bricks. Using 3D modelling software, the architects extruded the shape of the rose window in an imaginary cone back to an exact a point on the street corner, from where it is designed to be viewed – which happens to be right outside an espresso bar, so you can have a good gawp while queueing for your coffee. “The council was so supportive,” says project director, David Crosthwait. “We even talked about having a special paving slab in the street, directing people to look up.”

It is a simple (some might say crude) concept. But it was fiendishly complex to execute. A hefty steel frame makes the architectural acrobatics possible, with a series of big arched ribs holding shelves that support the 10 different kinds of specially shaped glazed bricks. “It’s like a big steel wine rack,” says Crosthwait. It looks eye-wateringly expensive, not to mention the extra embodied carbon of all the steel, but Plant says the additional floorspace that the gymnastic feat allows “makes a good return on the investment”.

The project is perhaps the most literal example of building around a sight line in London, but it stands as a microcosm of the city’s long tradition of picturesque planning, where buildings have been sculpted by a matrix of invisible ley lines, designed to preserve a range of cherished vistas.

For generations, the dome of St Paul’s Cathedral has been the hallowed point to which all else must bow, extending a radial web of protected views across the capital. The system was first developed in the 1930s by Godfrey Allen, then surveyor of St Paul’s, who drew up a grid of height limits around the cathedral, primarily to preserve views from the south bank – many of them from outside his favourite pubs.

The rules have since been expanded and codified in the London View Management Framework, which details the precise coordinates of the 27 protected views and 13 protected vistas – even taking into account the curvature of the Earth, so distant are some of the precious prospects. They are classified into four categories, including London Panoramas, such as the view from Parliament Hill; Linear Views, such as the Mall to Buckingham Palace; River Prospects, including the Victoria Embankment; and Townscape Views, including Parliament Square to the Palace of Westminster. But St Paul’s still reigns supreme, enjoying protection not only from buildings obscuring its foreground, but also from things popping up in the background – in theory, at least.

Conservationists’ eyebrows were raised in 2016 when it was belatedly discovered that the expensive shaft of Manhattan Loft Gardens, a 42-storey tower of luxury flats in Stratford, was poking up behind the dome of St Paul’s like a chubby middle finger. The fact that this was only visible through a telescope from a mound in Richmond Park, 20km away, where a hole is especially cut in a hedge to preserve the vista, mattered little to outraged critics with telephoto lenses. (The LVMF protected view stipulates the background should be protected up to 3km behind St Paul’s, whereas the tower is 7km away.)

More visibly, the odd shapes of many of the City of London’s skyscrapers are guided by their need to dodge the views of St Paul’s. The angular wedge of the Cheesegrater, by Richard Rogers’ firm RSH+P, is so shaped in order to lean out of the view from Fleet Street – fittingly, from just outside Ye Olde Cheshire Cheese pub. It was an engineering feat that took twice as much steel as the Eiffel Tower to achieve. Similarly the Scalpel, by KPF, leans in the opposite direction, sloping back to the south in a mirror-image incline, the duo lurching away from the dome as if caught in an awkward dance of social distancing.

Perhaps the clumsiest manifestation of all the St Paul’s restrictions comes from French architect Jean Nouvel. His galumphing One New Change shopping centre staggers to the east of the cathedral, twisting and turning its brown glass walls as if drunkenly trying to limbo beneath the height limits.

The story goes that the architect turned up to the first meeting with the planners holding an Airfix model of a Stealth bomber. Just as the form of the plane was modelled to avoid detection, so too would his building be deftly faceted to duck below the radar of the viewing matrix. It’s not hard to see why he was tempted to indulge in a bit of sculptural slicing. The City’s supplementary planning guidance positively encourages it, talking of how the height grid around St Paul’s actually represents “a complex three-dimensional surface of inclined planes and occasional ‘cliffs’ where significantly different sightlines coincide” – catnip to an architect struggling for ideas.

As Peter Rees, then chief planner of the City of London, said at the time: “There’s only one tool of development control that really works – and which I possess – and that is a low threshold for boredom.”

Three extra-time goals fired Leeds into the FA Cup fifth round with a 4-1 win at Championship rivals Plymouth. The substitutes Crysencio Summerville and Georginio Rutter combined to put the visitors 3-1 up before a 117th-minute own goal by Argyle striker Ryan Hardie capped a comprehensive Leeds win. They will now travel to Aston Villa or Chelsea on 28 February.

Leeds hit the woodwork twice in the opening 20 minutes of a hard-fought first half but the tie was goalless at the break. However their pressure eventually told in the second half as Wilfried Gnonto fired the visitors ahead in the 66th minute with a measured right-foot strike from the edge of the box which beat Conor Hazard. Gnonto benefited from a superb pass from Glen Kamara from the right.

Plymouth equalised after a 78th-minute Morgan Whittaker free-kick from the left. Whittaker’s dead ball reached the 18-year-old Tottenham loanee Ashley Phillips, who looped a cross over Illan Meslier to Brendan Galloway, who chested the ball home.

Seven minutes into extra time, Rutter put Summerville on his way to a brilliant individual goal as he cut in from the left before beating Hazard with a soaring strike. As Plymouth pressed for an extra-time equaliser, Summerville teed up Rutter to sweep home Leeds’s third goal in the 111th minute. Argyle’s misery was completed when Ilia Gruev’s corner glanced off Hardie and skidded past his own keeper.

Coventry will host Maidstone in the fifth round after their 4-1 victory against Sheffield Wednesday. Kasey Palmer, the Coventry player who was racially abused by a fan at Hillsborough in the Championship game between these two clubs last month, opened the scoring after three minutes with a driving run and finish inside the box.

Wednesday equalised seven minutes later, the 18-year-old Bailey Cadamarteri firing a low shot into the corner of the net. Yet in the second half the hosts took over, scoring three goals in only eight minutes. Two from the in-form Callum O’Hare put Coventry 3-1 ahead before the contest was effectively ended by Haji Wright’s strike on 58 minutes.

Coventry will now host sixth-tier Maidstone, the first team from outside the top five divisions to make it to this stage of the FA Cup in 46 years. Coventry are seventh in the Championship while Maidstone are striving for promotion in the National League South.

Southampton stretched their unbeaten run to 24 matches in all competitions with a 3-0 victory against Championship rivals Watford, including two goals from the France Under-21 international Sékou Mara.

Mara lashed home from an angle to open the scoring on 52 minutes before doubling Saints’ lead six minutes later with a spectacular strike from outside the penalty area, finishing off a fluent counterattack by Russell Martin’s in-form side. The Scotland international Ché Adams sealed the win 14 minutes from time by steering in Joe Rothwell’s free-kick. Southampton will visit Liverpool in the next round.

It was an event intended to mark the reinvigoration of rightwing conservatism. But even before the first speaker took to the stage on Tuesday morning, the Popular Conservatism group had splintered.

Of the four MPs billed to speak, just two were present – Liz Truss and Jacob Rees-Mogg. The former cabinet minister Ranil Jayawardena, regarded by some as a rising star of the Tory right, pulled out on Monday with a swipe at his fellow panellists. And Simon Clarke, another Trussite former cabinet minister, was removed from the line-up by the organisers two weeks ago after calling for Rishi Sunak to be ousted.

“This isn’t about the leadership of Rishi Sunak,” the director Mark Littlewood, who until recently led the Institute of Economic Affairs, told the room. “I’m personally immovable in my view that Rishi Sunak should lead the Conservatives into the next general election.”

But although none of the speakers openly questioned Sunak’s leadership, much of the rest of the event amounted to an evisceration of his policies.

The former Conservative party vice-chair Lee Anderson attacked the government over its approach to net zero. He called for coal mines to be reopened in the north of England and for people to be able to choose whether to pay green levies on their energy bills.

“We’re burning coal in our power stations but it’s foreign coal,” he said. “How is that contributing to net zero? It’s an absolute nonsense.” He also said his constituents weren’t “lying awake at night worrying about net zero”.

The parliamentary candidate Mhairi Fraser, who is standing in Chris Grayling’s safe Tory seat of Epsom and Ewell, launched an extended attack on Sunak’s smoking ban and the Covid lockdowns.

She said the ban would create a “ludicrous two-tier system where in the years to come a 50-year-old man will be able to legally buy his cigarettes but his 49-year-old wife will not”.

“Once one freedom is surrendered, other freedoms follow, because the state is no Mary Poppins,” she said. “Let us never forget the nanny in her most monstrous form – the Covid lockdowns .… It’s time to put nanny to bed.”

Rees-Mogg declared that the “age of Davos man is over” and Truss urged her colleagues to stop worrying about getting a job in Sunak’s government and take the fight to “left-wing extremists” running UK institutions instead.

Truss claimed these included “environmentalists” and those who are “in favour of supporting LGBT people or groups of ethnic minorities”.

Lord Gavin Barwell, former chief of staff to Theresa May, called for Truss to lose the Tory whip for those remarks. He said: “Liz Truss has done more than enough damage to the Conservative party already. She should apologise for this offensive nonsense or lose the whip.” This would force her to sit as an independent MP in the Commons.

The Popular Conservatism group also aims to pile pressure on the prime minister to cut taxes, to adopt hardline policies on immigration and to leave the European convention on human rights.

Many Tory MPs on the right of the party decided to stay away. “I’m not sure what space this is meant to fill,” one MP said privately. “The Conservative Growth Group already advocates libertarian economics. The Common Sense Conservatives talk about cultural issues.”

Meanwhile Kwasi Kwarteng – formerly Truss’s chancellor and closest political ally – pointedly decided to announce that he will not be seeking re-election as an MP.

One person who was present was the former Brexit party leader Nigel Farage, in his capacity as a GB News presenter. A few years ago, Tories found to be associating with him risked suspension from the party – but on Tuesday attendees were lining up to take pictures with him.

Farage said he was not seeking to join the Conservatives, “given what they stand for”, but he did not rule out standing for parliament with Richard Tice’s party, Reform. “I suspect I would agree with a lot of what is said on the platform this morning, but none of it is going to be Conservative manifesto policy,” he said. “Whilst there were some big names like Liz Truss, Jacob Rees-Mogg – I saw Priti Patel coming into the audience earlier – they are a very small minority within the parliamentary Conservative party.”

Labour and the Liberal Democrats mocked the new Tory grouping. The shadow paymaster general, Jonathan Ashworth, wrote to the panellists on Monday night asking whether they still supported unfunded tax cuts and the use of offshore tax havens. The Lib Dems published a social media graphic of the Top of the Pop[Con]s “greatest hits” – including Common (Etonian) People and It’s the End of the Tories As We Know It (And I Feel Fine).

Unfazed, Truss insisted; “Britain is full of secret Conservatives – people who agree with us but don’t want to admit it because they think it’s not acceptable in their place of work, it’s not acceptable at their school.”

Littlewood said the Popular Conservatives, or PopCons, would be taking their arguments to voters around the country. The response they get will be a test of Truss’s claims.