But now the dust and the feathers have settled, and there's a new building there. A big fat broody hen of a building. Its beaked head stares brightly and beadily across at the Mansion House, the Royal Exchange, the Bank of England. Its wings are folded neatly along its plump striped flanks. Its feet are tucked into a hole it has scraped in the ground. It fought to get there, it is happy there and it has absolutely no intention of moving. This is (the last and) most controversial building to be designed by the late Sir James Stirling.

With any other city block, an address is just an address. But the slender bronze characters spelling out "1 Poultry" on this one are akin to a campaign medal. This is the site that Lord Palumbo, property developer and former Arts Council chairman, had tried to rebuild since 1968, when as a young man he invited the great modernist Mies van der Rohe to create a tower and plaza there. Having painstakingly spent years piecing together the land to build it, he was then thwarted by a famous early 1980s public inquiry that rejected the scheme. Immediately, Palumbo invited Stirling, in 1985, to design something entirely different: no tower, no plaza, but a wedge-shaped block to fill the gap left by its Victorian predecessors - most notably the spikily appealing Mappin and Webb building on the apex of this triangular cluster. Stirling's design was finalised in 1988.

Another huge and lengthy battle erupted as conservationists fought to defend these remnants of the imperial heyday of London's commercial district. Finally Palumbo won: a salvaged terracotta frieze of 1875 by Joseph Kremer on Poultry, and the rescued Mappin and Webb clock inside the rotunda, are the only bits of the old to be incorporated into the new. But just as Mies had died before he could get going on the earlier scheme, so Stirling died unexpectedly in 1992, with not a stone laid. Those of a superstitious bent might be tempted to conclude that the place had a curse on it. But Number One Poultry was built. Palumbo devoted all his energies to it after quitting the Arts Council, while Stirling's partner Michael Wilford stuck as closely as he could to the posthumous design he had helped create.

It is, inevitably for a building designed 10 years ago, completely out of its time. Even when it was first presented back then, it was odd, for this was Stirling at the height of what, were he a populist, could be called his post-modern phase. Banded two-tone stonework in pink and brown, huge carved Egyptian cornices, great zig-zag industrial windows, a triangular lightwell rising up through the central drum, that curious beak-like tower at the prow, all manner of strange things happening on top and some strange semi-subterranean rumblings beneath - what was this place all about? What intellectual game was he playing? As that dangerous thing, an "architect's architect", Stirling was scarcely guaranteed to appease public opinion.

To visit the finished building today is to take a stroll around the recesses of Stirling's fascinating and complex psyche. It seems right that the building should be completed just as Mark Girouard's warts-and-all biography of the architect, Big Jim, is published. In the book, Stirling's libidinous antics are laid bare in a way that puts him on a par with other highly-sexed architects of genius, from Frank Lloyd Wright to Richard Rogers. Jim managed to be at once charming, intolerant, funny, coarse, shy, cultured, mischievous, stubborn, and introspective. To judge by accounts, he shared this volatile combination of characteristics with his English predecessors Edwin Lutyens, the great Edwardian country-house architect, and Nicholas Hawksmoor, master of baroque grimness, who acted as a muse to both Wren and Vanbrugh and went on to design churches of megalomaniac perversity. It is in this context that you have to regard Number One, Poultry. Stirling was a tricky customer in a tradition of tricky customers. His output was not safe, committee, stuff, and inclined to the monumental. You can no more ignore his buildings than you could ignore this mountainous man shuffling along the street.

It might seem curious that dapper, diffident Palumbo, after his love-affair with the glacial perfection of Mies, should have selected the rumbustious, untidy Stirling. He has no regrets: "I'm permanently starry-eyed about it," he says as we inspect the building and he exchanges greetings with the workers. Back then, Stirling had just completed what some regard as his greatest building, the 1984 Staatsgallerie in Stuttgart. It had re-established his then battered reputation after a run of bad publicity for earlier British work, which had a tendency to leak and fall apart. Despite the confined nature of the wedge of land at Poultry, Stirling offered a new variation on the big idea of Stuttgart: the central circular courtyard acting as a public route across town.