Museum of London Calling

Do you know where the Museum of London is? Even if you've been there, it's hard to say. The address is London Wall but you won't find a front door on that street. The grey brick rotunda on the corner of Aldersgate Street and London Wall has the white lettering of the museum emblaz-oned on it, but when you're next to it the route inside isn't obvious.

The 1976 museum, dedicated to a chronological history of our capital, is about to reopen its galleries in full to the public. For the past three years, while the upper rooms have remained open, taking visitors as far as 1666 and the Great Fire, the lower areas have been closed while the new £20 million Galleries of Modern London were built.The scope of the displays has been brought beyond the outbreak of the First World War, where it stopped before, to the present day. The completion of this phase is the end of a decade of work, adjusting the museum to give it more exhibition space, an education centre and a new entrance.

The surgical task of redesigning this tricky building has been carried out by Wilkinson Eyre Architects, twice winner of the prestigious Stirling Prize (the second of these for the blinking bridge in Gateshead, its iconic calling card). Despite adulation from peers and plenty of work from developers, it's arguable that the London practice, unlike Foster, Rogers et al, has yet to design a building in the highest rank of British architecture.

This project isn't that masterpiece, but in its careful modesty it demonstrates a respect and understanding of modern architecture that I feared might have been lost as the office grew bigger. Wilkinson Eyre's work has changed for the better the museum's relationship with the public realm and inside has created rational new galleries, which the museum has filled with its characteristically exuberant exhibition design.

The Museum of London, created by modernist architects Powell Moya and Partners at the south-west corner of the Barbican, was called by one of its original critics "the most retiring public building in London". This is probably because of the painful journey to get into it. Intrepid visitors must locate the escalator on the south side of London Wall, cross over a bridge above the busy road, enter the brick rotunda and process around a circular walkway before finally being delivered into the forecourt and entrance. Wilkinson Eyre created a new, larger, glass hangar of a reception area in 2003, which has improved the experience of arriving, but this has not solved the inherent problem of this hidden, high-level entrance.

It might seem perverse to refuse to have an entrance at street level but it wasn't entirely the architects' fault. In the Sixties and Seventies, the City of London decided to create a system of "high walks", separating pedestrians and cars, supposedly for mutual bene-fit. The City is still committed to this policy where the high walks exist, and the Barbican complex is the most complete example. However, while Wilkinson Eyre was not able to do anything about the location of the doorway, it has made a big effort to animate the street below with a new staircase tower in Aldersgate Street and a huge new window facing London Wall.

The museum's director Jack Lohman, who has overseen the improvements for the past eight years, told me: "Nobody would design a building with an entrance up in the air, so the building starts with a great disadvantage. We need to think differently about how it connects with the city." The shop window is key to this thinking. Behind it to attract attention is the museum's most famous exhibit — the red and gold magnificence of the 18th-century Lord Mayor's coach.

In terms of what's on show, there is now a lot more to remember than just the histrionic Great Fire of London audiovisual and the coach. The Museum of London still has a large in-house exhibition design department (rare for a contemporary gallery), and the curators know their material. While museums like the V&A and Tate employ tasteful young architects to create cool-looking displays, the Museum of London is unashamedly popular (nearly 400,000 annual admissions before the partial closure) and doesn't mind hamming it up to inform its visitors.
A new staircase leads down to the Modern Galleries, which are absolutely full of stuff, with vitrines in the floors and walls, objects in cases, on plinths and behind glass walls, interspersed with frequent audiovisual displays adding further depth and richness. It might not be trendy minimalism but it is addictive, and the elaborate Aladdin's cave effect has some wonderful moments.

My favourite is probably the fabulous placing of some late 18th-century Coade stone sculptures. The neoclassical figures, originally placed above the door of an insurance office in the City, have been given a perch on top of one of the exposed concrete structural beams of the museum. The fine texture of the Coade stone contrasts with the rough concrete but the colours of the two materials are almost the same, creating an almost geological connection between object and building.

The best new exhibit is the interior of an early 18th-century prison cell, complete with detailed graffiti, which is now arranged in such a way that you can walk inside and study at close hand the barely sane scrawlings of its various inmates. That and an extended series of Victorian shop fronts stick in the memory more than some of the new and flashy presentations, which, while appealing to younger audiences, are nothing that hasn't been seen in the Science Museum's Wellcome Wing.