They will either give the thumbs-up or pronounce a death sentence on Daniel Libeskind's proposed pounds 75m extension to the Victoria and Albert Museum. It is generally agreed that The Spiral, on the site of the museum's former boilerhouse, will be the most remarkable building that London has seen for many years. And that is part of the problem. Kensington's planning officers have submitted their recommendations for tonight's meeting - that the answer should be a flat no. The assembled councillors must now decide whether to heed that advice, or to take an un-British walk on the wild side.
Either way, the decision is historic. Libeskind's quirkily angular building - a kind of architectural sculpture - beat off competition by Sir Norman Foster and others to be chosen for the site on Exhibition Road. The V&A was thrilled with the proposals, arguing that the building will be "an icon for London". Alan Borg, the museum's director, argues that the failure to approve The Spiral ("a key which unlocks this very complex site") would send a disastrous message. "I can't believe that we - London or the country - can let slip an opportunity to do something as important or exciting as this. If it doesn't happen, it will be a serious indictment of our engagement with modern art and architecture."
There has been support from what might seem to be unlikely quarters. English Heritage (self-described "reactionary old fuddy- duddies") took out advertisements praising this "superb design of outstanding innovation" and the "powerful sculptural qualities which would add interest and drama to the variety of historic buildings in Exhibition Road". The Royal Fine Art Commission supported the "daring and innovative structure", and pointed out that the V&A was founded with a strong emphasis on contemporary art and design. "The Commission therefore considers that it is appropriate that a new building there should be an expression of its own time."
Local groups have, however, been up in arms from the start about the plans for The Spiral. The Knightsbridge Association complained that the Libeskind building is "a classic example of architectural bad manners". Elsewhere, too, there have been loud catcalls. The Evening Standard's Brian Sewell fulminated against this "unsuitable", "grotesque", "appalling", "beastly" building. And so on, in a steady stream.
All this venting of British spleen against the architecturally different has a history, of course. It was in 1984 that the Prince of Wales launched his dramatic broadside on modern architecture, with his description of the proposed National Gallery extension as a "monstrous carbuncle" . "That's one decision I won't have to make," as the then environment secretary Patrick Jenkin remarked that night. The Prince's own taste is for architectural pastiche.
It is, however, unclear whether such princely disdain for the different is unchallenged in 1998 Britain. Sneers about monstrous carbuncles no longer strike such a powerful chord as in 1984, when Britain still felt deeply alienated by the who-cares-about-the-public attitudes of urban planning in previous decades.
Libeskind himself - a Polish-born American who studied in London and now lives in Berlin - is dismayed, but not surprised, that the Kensington Fourteen are being advised to say no. "[The planners] didn't have the courage - bureaucrats often don't - to see this as a challenge and a hope for Britain of the future." At the same time, he believes that the concept of The Spiral returns to first principles. "It erases the 20th-century division between engineering and architecture. Arts, crafts and science go forward as a unity. It is an articulated space and part of the process of inspiring people." He talks of this as a "wholly unprecedented building", but argues: "I think times have changed, people have moved on."
Paradoxically, even the planners acknowledge the power of The Spiral: "The building is clearly of a very high quality of design, and if built, would become a national landmark." In effect, the nub of the argument for refusal is that The Spiral would draw too much attention to itself (the same argument which was used against Wren's design for St Paul's).
Whichever way tonight's decision goes, the V&A hopes that the tide of history is with them. If Kensington says no, the case will go to appeal, when John Prescott will have the last word. Borg argues: "Buildings have their moments. And this is absolutely the moment... It's the final chord of the symphony."
Previous form suggests some hidden reasons for optimism. Many of the project's critics are keen to praise modern buildings elsewhere, including the new Guggenheim Museum in Bilbao, the pyramid at the Louvre, and Libeskind's own best-known project, the jaggedly astonishing Jewish Museum in Berlin. Each of these buildings is now acknowledged to have been enormously successful. But it was not always thus. There was no shortage of critics of Frank Gehry's Bilbao project in the early stages. The museum was accused, too, of ludicrously inflated expectations when it suggested that it might attract 400,000 visitors in the first year; in the event, more than three times that number came.
IM Pei's Louvre pyramid ran into endless difficulties with the Paris planners, who (like the Kensington planners, with regard to The Spiral) believed that the design was too big for the site. The architects had to build a full-scale model of the pyramid and winch it into place by crane to persuade the doubters to change their minds. Berlin politicians, too, initially voted against Libeskind's project. One of the recent prizes that the building has won comes from the city of Berlin itself.
By contrast, it would be nice to think that London might get it right first time. The architectural terror instilled by the not-quite King Charles III (off with their modernist heads!) means that almost no buildings of any interest, let alone international renown, have gone up in London in recent years. If we are lucky, that could all be about to change. The councillors in Committee Room 1 hold the key.