Suddenly, such places are everywhere. Of course, one thinks of Norman Foster's Great Court at the British Museum, not only for the central public space it creates but also for the new pedestrian route across Bloomsbury, through the heart of the Museum, that it opens up. But you think also of Rick Mather and BDP's glazed courtyard at the National Maritime Museum in Greenwich, of Mather's smaller cafe-courtyard at the Wallace collection, of his sequences of outdoor spaces at the Dulwich Picture Gallery or of his masterplan for the South Bank arts complex. Look to Manchester, where a series of new public open spaces of Victorian confidence and magnitude, by landscape designers EDAW, have resulted from the post-bomb reconstruction process. Look to Birmingham, which has quietly been repairing its wrecked urban fabric in this way, piece by piece, for years now. Look to Armagh in Northern Ireland, where the new Market Place arts centre by a rising young architect, Glenn Howells, is based on the concept of a sequence of enclosed and open public spaces stepping down the hill. Look to Somerset House in London, where Sir William Chambers' forgotten urban square has been restored and reopened to the public, or Newcastle, where part of a former traffic canyon is being turned into a new square by designer Thomas Heatherwick.

Even the furthest-flung reaches of London's docklands are now being provided with a healthy number of new parks and squares - elements largely absent from the unregulated early phases of the docklands project. What with all these and the numbers of new pedestrian bridges all over the country - inland piers, essentially, since the viewpoint they provide is as important as the means of crossing - it's good news for strollers and creative loiterers everywhere. But why exactly is this happening now?

Certainly the Lottery money - which means public money - has helped. When architecture is commissioned on a strictly commercial basis, public space is too often neglected because, actuarially speaking, it seems not to generate revenue. Which is nonsense, because anything that attracts people generates revenue. But there's more to the phenomenon than this, and it extends into areas of design other than architecture. The old notion of extreme efficiency at the expense of space and comfort - think of Concorde, or the now-axed cross-channel hovercraft, or the utilitarian trains of the British Rail era - is being overtaken by something more relaxed. The forthcoming subsonic Airbus A3XX with its airship-like public areas, or the next generation of Virgin trains with their shops and cafes (interiors of both of these by British designers Priestman Goode) is more the thing. As are today's enormous cruise-liner-like cross-channel ferries, offered as an antidote to the old-fashioned functionalism of the Channel Tunnel. True, our railways are leisurely for the wrong reasons right now, but that will be fixed: the new Virgin trains, assuming they work, will be faster as well as pleasanter.

So there is an expansive, public-spirited mood to be caught. Is there cause for optimism at the start of the 21st century - the century when cities will either save us or strangle us? It is dangerous to extrapolate too far - the British enthusiasm for civic improvement often comes at centennial moments, and usually does not last. So let's make the most of it while it does. Two projects in particular, at the turn of the Millennium, make me want to wave and cheer because of the way they lift their utterly different environments. The first is a little footbridge across a road called Plashet Grove in London's East Ham, connecting two halves of a secondary school. It could have been numbingly utilitarian: instead it is a joyful affair of asymmetrical hoops, culminating in a sitting-out space - a modern gazebo - in the middle. Its architects are the richly original and too often thwarted Birds Portchmouth Russum, engineers are the very creative firm of Techniker. Together they've done a blinder, in just the sort of place you least expect to find it.

The second is a new urban monument in O'Connell Street, Dublin - finally approved by the Irish government at the very end of 2000. Part of a package of landscape improvements to this great but decayed street, it will be a simple but awe-inspiring slender spire of stainless steel, nearly 400 feet high, by architect Ian Ritchie. Previously there was a Nelson's column on the site, efficiently removed by the IRA. But Ritchie's Spire of Dublin, like the observation wheel of the London Eye, will be a monument to no individual or event. Let's hope that such initiatives mark a new age of urban elegance for its own sake: the age of the flâneur.