LONDON -- London is still in shock from the runaway success of the new Tate Modern Gallery in the former Bankside power station. Despite its vast size, the building is packed, sometimes almost too packed, with visitors whose numbers will probably hit at least four million in the first year, double what had been expected.

The success of the Tate Modern, though, should not be allowed to obscure an even more mpressive story: if there has been one consistent architectural theme in London in the remarkable millennial year that has just passed, it is not the opening of new museums but transformations of the old.

Take the Wallace Collection, just off Oxford Street in central London, a stunning mix of the best Svres china and French 18th-century furniture in the world, superb Old Masters (including Frans Hals's "Laughing Cavalier") and an impressive array of arms and armor. This remarkable collection, which was amassed over several generations by the fabulously wealthy Hertford and Wallace families and is still housed in their former London house, would be any other city's pride and joy. But in London it has been overshadowed by the better known national museums.

Now, thanks to a $15.9 million overhaul, largely financed by the National Lottery and completed last year, the Wallace Collection is beginning to attain its rightful position. The once-dank central courtyard has been transformed by an airy glass roof designed by an American architect, Rick Mather, a long-term resident of London. This new light-filled atrium or winter garden is now occupied by the restaurant that the Wallace Collection had always lacked. Beneath it is a lecture hall, with education rooms, library, a gallery for the reserve collection and a temporary exhibition space all of them new.

At last the Wallace Collection, which until now has had hardly any space beyond its primary galleries, has the room and facilities to make the most of its great collection. The result is impressive. Already visitors have tripled.

Or head south into the inner suburbs, to Dulwich, which still retains the feel of a village on the edge of London, even though the metropolis now stretches far beyond it. It is the home of the Dulwich Picture Gallery, England's first deliberately constructed public art gallery. Designed by the great early-19th-century Classical architect Sir John Soane, it has long been held in great affection by those who know it, though they have been relatively few. The gallery's finances were recently so dire that it nearly closed because its owner at the time, the independent boys' school Dulwich College, could not afford to run it. As for the building, though Soane's pioneering use of toplighting (natural lighting from above using skylights) was an inspiration to museum designers, it suffered as badly as the Wallace Collection from lack of supporting facilities.

Today, the Dulwich Picture Gallery, now an independent charity, has been transformed at a cost of $13.5 million, also with help from the National Lottery and, again, to Mr. Mather's designs. A new courtyard has been created in front of Soane's building, in addition to a new cafe and lecture hall and markedly better conservation facilities. In the viewing galleries, rotting skylights and inadequate air-conditioning and lighting have been replaced, and handsome oak boards have taken the place of the dreary 1950's cork flooring.

In both cases Mr. Mather's approach has been marked by sensitivity and a sense of restrained understatement that seems to fit with his dry, understated personality. Where other museums and architects have been trying to grab the public's attention with ever- more striking architectural set-pieces one thinks in particular of Daniel Libeskind's proposed spiral for the Victoria and Albert Museum in London Mr. Mather's work at both the Wallace Collection and the Dulwich Picture Gallery leaves the original structures pre-eminent. The result is like a precious drawing that has been carefully cleaned and remounted. Though at first you barely notice the difference, the original is subtly and significantly enhanced.

As the Wallace Collection is surrounded on four sides by streets, Mr. Mather's options were limited. To find the space he needed, he was forced to dig under the courtyard and the building's wings and to open up the basement of the original house. The new interiors follow a simple modernist aesthetic and are in no sense a challenge to the original galleries. The same is true of the roof of the courtyard, which has been kept as simple as possible to avoid drawing attention to itself.

Mr. Mather's approach provides the existing galleries with the resources they need to work effectively in the 21st century while not upstaging them. Indeed, the work has gone hand-in-hand with the steady restoration of the original decoration of the galleries. At the Wallace Collection, as at so many long-established museums, the 20th century saw curators fighting against the building they occupied. The sense that the Wallace Collection was originally a plutocrat's house had been lost as curators tried instead to make it into an anonymous museum where the objects were supposed to speak for themselves.

For Rosalind Saville, the enthusiastic director of the Wallace Collection who has masterminded the recent work, this was quite wrong. To her the public could only really understand the collection in its original setting, so room by room she has been recovering the original glamour, hanging heavy silk curtains, putting back rich fabrics on the walls, banishing the banal detritus of a conventional museum.

At the Dulwich Picture Gallery, Mr. Mather faced an even greater problem. Soane's gallery has become an iconic building to Modernist architects who see its stripped Classical manner as one of the precursors of the Modern movement. Any alteration or addition was likely to raise howls of objection. What Mr. Mather chose to do was develop an unexecuted idea by Soane for a courtyard in front of the gallery.

Approaching the gallery from the street, there is nothing to suggest a major new wing of a museum, just a blank wall made of rough, hand-made bricks similar to those used on the gallery, topped by a thin, Soanean cornice, which hints at what lies behind. This restraint is continued inside the courtyard, where the new buildings lie behind a glazed, cloisterlike corridor, which will seem more like an enclosed garden walk than a building when wisteria has grown over the uprights. The new rooms that open off it were kept as low as possible to minimize their impact, but by subtle use of Soane-inspired toplighting, Mr. Mather has avoided their seeming too low.

At a time when architecture is once again caught up in an obsession with dramatic signature buildings "astonish me" appears to be the catch-phrase clients throw at their architects Mr. Mather's work at the Wallace Collection and the Dulwich Picture Gallery shows that quality and significance are not necessarily a function of visual impact.

But the transformation of the two museums also highlights another, far-reaching phenomenon. In the rush to create new attractions and museums, which has been particularly marked in the splurge of building that has followed the creation of the National Lottery in Britain, novelty has been praised above all. The revived Wallace Collection and Dulwich Picture Gallery show what happens when we look with fresh eyes at what we already have in the case of the arts in Britain that means great collections and impressive buildings and then ask how the full potential can be achieved.

In most great museums, particularly those in London, that does not mean new galleries or new objects, important though they may be, but the facilities to unlock the potential of existing collections, education rooms for children and adults, lecture halls, proper conservation facilities and attractive cafes and restaurants.

The same approach can be seen elsewhere in London at the National Portrait Gallery; the Geffrye Museum in the East End, known for its furniture and period rooms; and, most dramatically, at the British Museum, which reopened last month after a $150 million transformation. Other major museums have similar plans. Next October, Tate Britain, the original Tate Gallery at Millbank, will open a new entrance, new galleries and new ancillary spaces at a cost of $54 million. The two national galleries, the National Gallery in London and the National Gallery of Scotland in Edinburgh, have also recently announced ambitious improvement projects. The National Gallery in London is about to start on a master plan that will open up the ground floor, until now largely used by the staff, to the public. The National Gallery of Scotland will take over the adjacent Royal Scottish Academy and create an underground link to it from the current gallery.

If the main thrust of 20th-century architecture was about clearing the ground and creating something new, the Wallace Collection and the Dulwich Picture Gallery suggest a very different approach for museums and the cities they serve in the 21st century. Perhaps this will turn out to be a century in which people are confident enough to be modern but also confident enough to value the best of the past.

Giles Worsley