Look what they’ve done to the Whitechapel

Now, more than a century after it was first conceived, the Whitechapel has got back in touch with its roots. When the gallery reopens in two weeks' time after a £13.5 million refit, visitors will find the space has doubled in size, by absorbing a neighbouring former library, to make more galleries, more space for school parties and adults to experience art and create their own, and to ensure that there is always at least one free exhibition on show.

Yet the redesign is not a work of expansive cultural machismo, not an iconic monument designed for blockbuster sculptures and installations. The new Whitechapel has subtler ambitions. As conceived by Iwona Blazwick, director since 2003 and driving force behind the expansion, the new gallery will remain faithful to its founders' "art for all" ideal. This is a building that strives to connect with the part of London in which it stands.

The reconstruction is so discreet that from the street you would hardly know it had changed. The two façades, gallery and library, remain distinct, with Aldgate East Underground station between. Inside, it's the work of nudges and nuances rather than grand gestures - for the laudable approach of the Belgian architects Robbrecht and Daem and the London practice Witherford Watson Mann, with artist Rachel Whiteread as an active collaborator, has been to bring the best out of the exceptional buildings already there.

The original gallery was designed by Charles Harrison Townsend, one of the great underused talents of British architecture, whose genius flickered to life here and in two other memorable façades: the Bishopsgate Institute and the Horniman Museum in Forest Hill.

Townsend built his gallery as two plain halls, one on top of the other, behind a playful, freeform, turreted façade that is as near as English architecture ever got to Art Nouveau. Clad in terracotta to resist the filthy London air, it remains a billboard of optimism, with foliage etched in shallow relief, to evoke a healthier, more idyllic life than that which surrounded it. In keeping with the Barnetts' principles of accessibility, Townsend avoided porticoes, steps and forecourts, and sat his gallery right on the street, jostling with tailors and cafés, and the floor ran straight from the pavement to the main gallery space, without change of level.

In the last refit in 1985, when Sir Nicholas Serota was director, a café, office space and a mezzanine-level gallery were added.

Now the neighbouring Passmore Edwards library has been joined, and in such a way that the two buildings keep their identities but connect happily. Another work of late Victorian philanthropy, the library became the "university of the ghetto", a focus for Whitechapel's refugees from Russian pogroms and a place that nurtured Jewish intellectuals and radicals. The area's Jewish population has almost all moved on and the library has relocated to the David Adjaye-designed "Idea Store" further up the road.

The spaces that expansion has allowed include an "education and research tower", new galleries to show works from public and private collections, a home for the gallery's archive, a new restaurant and a new-commissions gallery which, like the Turbine Hall at Tate Modern, will house long-lasting installations by invited artists. Before the expansion the Whitechapel had to close for at least 10 weeks a year while it installed exhibitions. Now the extra spaces will ensure that there is always something to see.

The architects' approach has been to retain fragments of the old, such as Victorian balustrades and, in the commissions gallery, walls of yellow London brick, while inserting the new alongside. Old and new are allowed to co-exist rather than being orchestrated into some grand composition. The urge to make everything neat and tie up loose ends has been resisted.

Townsend's original building was enlightened and democratic, but also church-like and inward-looking, with a faint whiff of preaching that reflected the fact that one of its founders was a canon. The new version is more like a big house, where you can wander from room to room rather than follow a prescribed route. Windows open up views to the surroundings, whether beautiful or not, from Hawksmoor's magnificent spire of Christ Church Spitalfields, to the rickety roofscape of adjoining buildings, to a truly repulsive new Ibis hotel, which somehow slipped through the local planners' net. It culminates in a rooftop classroom for visiting school parties, where, as the architect Paul Robbrecht says, "all of a sudden you experience London again".

In the past the gallery did an efficient job of delivering single exhibitions - its greatest hits include the only showing in Britain of Picasso's Guernica in 1939, the first major shows here of Jackson Pollock, David Hockney, Gilbert and George, and Richard Long. There is no reason why the Whitechapel should not continue a programme of significant shows but the new layout offers a looser, more varied experience.

At times you sense a lack of urgency: there is a feeling that some of the galleries exist because there was space to be filled, rather than that they were truly desired. Sometimes, amid the gallery's sensitivity and subtlety, you wish for another moment of exuberance like Townsend's façade. But there hasn't been much subtlety in architecture recently, so the revamped gallery is erring on the right side.

The expanded Whitechapel is the third gallery or museum this year to make a virtue of leaving things alone. The others are David Chipperfield's magnificent remaking of the ruined Neues Museum in Berlin, and 6a Architects' Raven Row gallery. Clearly it's the trend of 2009 and, as there has been an overdose of shiny novelty in recent architecture, it's a welcome adjustment.