Adding something to a Soane is one of the most difficult architectural acts in the world. Rick Mather has complemented the wonderful Dulwich Gallery with grace.

The Dulwich Gallery is wonderful but weird. Strange from the first, it was set up to house a collection of seventeenth- and eighteenth- century paintings built up between 1790 and 1795 by Noel Desfans and Francis Bourgeois for Stanislaus Augustus, the King of Poland. Unfortunately, by 1795, the kingdom of Poland had ceased to exist, so the collectors were left with a splendid collection with nowhere for it to go. Efforts to sell it to the Tsar or the British Government came to nothing. Desfans died in 1807, and, apparently on a whim after a day's enjoyable visit to the south-east London school, Bourgeois decided to leave the lot to Dulwich College (a seventeenth-century foundation that already had a small collection left by its founder, the theatrical entrepreneur Edward Alleyn). In his will, he made three other important provisions. First, his friend John Soane should be the architect. Second, the gallery should include a mausoleum for him, Desfans and Desfans' wife, Margaret, whose money seems to have financed the collection, and was the third member of an amiable but rather scandalous menage a trois: they were to be united in death as in life. The other requirement was that there should be almshouses for six worthy ladies. Soane's building was set separately south of the rest of the college complex, a jumble which reflected the institution's rather chequered history. In essence, Soane made an enfilade of five top-lit galleries with, to the west, an attached strip of almshouses. The mausoleum dominated the east-west axis from the entrance. Now, the building is a good deal different from the one opened in 1817. Externally, Soane's building was deceptively simple: symmetrical in blind arcaded brink. The almshouses became part of the gallery in the 1880s. Between 1909 and 1939, E.S. Hall arranged five new galleries along the east front, so almost completely obscuring Soane's entrance elevation. A porch was added by Austin Vernon. In 1944, a bomb hit the place (luckily the pictures had been taken away), and the gallery and mausoleum were restored in the immediate post-war period, when economy and Modernism were both driving forces.

Everyone revered Soane's Dulwich, which was the first public gallery in England, but by the beginning of last decade, it was clearly in poor repair and inadequate to house the collection. Space for the gallery's excellent education programme was needed, as was a workshop and storage. Money (£5 million) became available from the Heritage Lottery Fund, and £3.8 million was found from an appeal. Rick Mather was appointed as architect because his competition design made least impact on both grounds and existing gallery, and linked it elegantly to the Old College complex.

The main armature of the design is a bronze and glass cloister, which links all the new elements and connects them to the Soane building. It takes its height, and to some extent its proportions, from the College Chapel (an 1830s reproduction of Alleyn's original). Its roof lines up with the transoms of the chapel windows and its vertical elements echo the old building's buttresses. An external bronze frame supports a brise-soleil - the main glass walls face south and west. The frame is also intended to act as a sort of pergola to support wisterias. (Is this wise? A mature wisteria will surely be able to bend the bronze). Transparent slots in the roof echo the rhythm of the paired mullions; they are mirrored in the York stone floor by green glass strips which light up at night. In summer, half the big glass panels can be slid open for cooling and allow people to walk out onto the close-cropped lawn. The cloister connects all the new spaces and forms a court in front of the Soane building. Main access to Soane has always been from College Road, to the east of the site, and the 1952 gates have been retained, though set back from the road. To their right is a new wing of accommodation, built up to the edge of the site. You can get to the Gallery either by going straight up the path to its front door, or taking the cloister which is entered to the right. it connects, first, the cafe, which looks out over the green and parkland to the south through a glass wall which can be opened onto the terrace.

Next comes the Linbury Room, a gallery and reception space which has jacks under the floor to allow it to be stepped into a lecture theatre or even performance space. There is homage to Soane here with a shallow domed ceiling (formed in fabric) surrounded by skylights which pour light down the walls. Further along the cloister, before it turns left in front of the chapel, is a lavatory block, This, the Linbury and the cafe are expressed to College Road in blank walls of modern hand-made bricks set in English bond with flush pointed lime mortal.

Craftsmanship is excellent, but some are worried about the reddish colour, which the architects claim echoes that of the original wall. A brilliant touch is the introduction of glass slots between the individual rooms which allow you to look from the street right through the block and cloister to the green court. Soane would surely have approved of such coups de theatre. En route to the Soane building, the cloister takes you past the chapel wall, then a teaching room (behind which are the stores and administrative spaces) before turning left to deliver you to the north-east bay of the Gallery. Of course, this is not the way in which Soane meant you to enter his building but, then, the bay was not there in his time (it was part of E.S. Hall's additions).

In fact, the new access has allowed the 1952 opening at the north end of Soane's enfilade to be blocked up, so that the character of the dense original nineteenth-century hang could be recreated, with Guido Reni's Saint Sebastian as the climax of the south-north axis. The enfilade has been gorgeously repainted in Soane's 'picture gallery red', traces of which were found under subsequent redecorations.

In the mausoleum, bomb repairs destroyed all traces of original paint and a stone stippled effect has been introduced, based on the hall at Pitshanger Manor, Soane's country house (AR January 1989). Specially made green Ottoman silk lines the galleries in Hall's east range making them intense and intimate, proper settings for smaller pictures like Dutch landscapes and flowerpieces. Windows made in Hall's wall have been blocked up, and the whole exterior has been re-ordered to become a replica of Soane's original east elevation, with blind arcades reflecting the panels in the attic behind (which is of course real Soane).

Soane's gallery has always had enormous importance because it uses daylight wonderfully. But his rooflights were almost all rotting, and those over Hall's galleries blocked views of what remained of Soane's east elevation behind. Mather's with Lighting Design Partnership, redesigned the lot. All skylights have double glazing with fixed louvre shading between the outer security glass and the inner frosted panes. Louvres are to prevent direct sunlight, run east-west and vary in angle according to the pitch of the light. Soane's lanterns have vertical as well as pitched panes, and the same double-glazed system has been employed there, but instead of fixed louvres, there are automatically adjustable opaque blinds. As a result of all this, Soane's lighting effects are reproduced (as far as we can understand them), and the problems of exposing pictures to the light of the heavens are minimized (the sloping glass will be adapted with films if experience shows that light levels are too intense).

Mather's scheme for Soane has to be judged by the highest standards. It is an almost complete triumph (almost because, when I visited it, there were still a few imprecise details, but perhaps these can be corrected during snagging). Mather has evoked Soane's spirit inside the poor tormented nineteenth-century building; he has done justice to Hall, and has made the great gallery part of a generous and welcoming public place. P.D.