Redesigning the bridge gingerly to sidestep such potentially deadly obstacles was a hugely costly exercise. It looked dead in the water. Fortunately, the project was saved by London’s new mayor, Ken Livingstone, who injected the necessary extra £16.7m to get the project moving again. If he achieves nothing else of note during his term of office, we should remember him for this, and for pushing through the forthcoming partial pedestrianising of nearby Trafalgar Square, in a Foster-designed scheme that leads naturally to the new Hungerford bridge. Some of Mayor Ken’s other traffic plans for London may be questionable, but not these.

So after all these delays, here it finally is. The upstream bridge is there, and is already making a palpable difference. There’s a promenade feel to the river crossing now - though puddles, the curse of the old rat-run of a crossing, are annoyingly present on the stairs and landings of the new one as well, though not on the well-cambered main span. This may be dealt with under the “snagging” clause of the building contract. On the north side, the new bridge hops across the Embankment road and descends into Northumberland Avenue, which leads up to Trafalgar Square. On the south side, it leads you to the Eye, so forming a tourist loop which takes in Westminster Bridge and Big Ben. When the downstream side is completed, that will set up a different loop that takes in Covent Garden, the South Bank, Somerset House and Waterloo Bridge.

Not everything is quite as Lifschutz originally wanted it. Walking the bridge on a perfect sunny morning, he pulls out the plans which show his original spur bridges branching off in two directions on the south bank - one going directly to the Eye, the other to the Festival Hall and points east. Apart from making more direct connections, these would have had the effect of shortening the apparent length of the crossing by providing more variety. Big new bridge landings for the spurs have however been built in the river, and the suspension masts form gateways at this point to indicate where they should go. In the future, they can be added. But as we know, the future takes a long time to happen in Britain.

There are other losses, mostly due to cost-saving, partly to security worries. For instance Lifschutz - one of the more inventive of our younger architects, and one of the least inclined to settle into a middle age of bland office-block design - has also been denied his transverse connection between the two new bridges. This would have passed beneath the railway through the mysterious chambers of Brunel’s “Surrey pier” standing out in the river. So a further potential richness has been postponed, perhaps for ever.

Luckily, Lifschutz Davidson’s design is strong enough to take the cuts with good grace, while still allowing the possibility of further change. In that sense theirs is a gothic, accretive approach: it contrasts strongly with the classically-pure solution of Foster’s bridge at Bankside, which is an all-or-nothing design.

Saved by this flexibility, new Hungerford Bridge succeeds in being classy public architecture. Public in the best sense: seven million people a year are expected to use it once both sides are open. It will change the way we perceive and use London. It removes some of the lingering isolation of the South Bank, it makes a new public space out of nothing. In terms of architecture doing the greatest good for the greatest number, this scores highly.