Galleries of Modern London, Museum of London, London

Previously hidden amid the Barbican complex, the story of the capital's history at last has a decent platform

When the Museum of London decided four years ago that it was time to revamp its Galleries of Modern London – the entire lower-ground floor, covering the Great Fire to the Great War – the nation's museums were still basking in a golden age.

Lottery money and a sympathetic Labour administration had made ambitious renovations almost commonplace, and the free admission introduced by Labour meant there was no shortage of visitors. Now refurbished at a cost of £20m – and divided into Expanding City, People's City and World City – the galleries are reopening in a very different climate. Fortunately for the Museum of London, theirs was a project that just slipped under the wire.

The challenges the galleries faced were many. Formerly, the displays had stopped at 1914, so there was nothing about the wars, immigration or recent cultural revolutions; concepts and technology were also outdated. Then there was the building itself. Marooned in the City, the Museum of London is ostensibly part of the Barbican Centre and just a short hike from St Paul's, but too far from either to benefit from passing trade. The problem is compounded by unfriendly Barbican architecture, which sites the main entrance one storey up and hidden behind a brick roundabout.

The museum has attempted to overcome this by creating a small City Gallery alongside London Wall, with a window at road level through which can be viewed the museum's single most distinctive item, the Lord Mayor's gold state coach. Solid and gaudy, the coach was made in 1757 and is still used every year for the Lord Mayor's Show. It should certainly catch the eye of passing motorists.

The galleries begin with Expanding City, covering 1670 to 1850, where the centrepiece is a wooden printing press that spews electronic headlines, a startling anachronism used to stress the city's growing literacy. There are other grand objects here, most notably a rebuilt prison cell from 1750 complete with poignant graffiti by inmates. But the smaller details also impress, such as the glass-topped inserts in the floor, displaying old clay pipes and other bric-a-brac that might seem too insignificant to warrant the standard glass-case treatment. And the way in which some items – a magnificent lady's dress, say, or an elaborate doll's house – are linked to their original owners brings a welcome personal touch.

Another embellishment is the theme that can be traced throughout the galleries, of trade, empire, colonisation, immigration and globalisation – in short, what London has done for the world and what the world has done for London. The best example is a map that shows trade routes and imperial expansion, which you move through time not by touching a screen but by turning a handle – a nice retro touch.

Speaking of which, one of the few pre-refurbishment items to survive intact is the museum's life-size walk-through Victorian arcade, complete with shops, pubs and, er, urinals. This is joined by a boisterous recreation of a Victorian pleasure garden, used to showcase the clothing in the collection. This lively space contrasts with a sombre, black-painted room in the opposite corner of the museum, where a German bomb is suspended from the ceiling and where visitors listen to recordings of Blitz survivors recounting wartime experiences.

Between these two extremes comes the People's City gallery (1850-1940), with much attention paid to the social divide. There is intelligent use of photographs and everyday items, while an entire room is devoted to Charles Booth's poverty map, an extraordinary 1888 endeavour which colour-coded every street in London according to its level of wealth. (Booth, a rich businessman, had set out to prove that poverty and squalor were less widespread than believed. In fact, his map showed the opposite.)

The museum's collection of suffragette paraphernalia is worth seeing, and segues into scattershot coverage of early 20th-century protest in general. Here are posters promoting communism, fascism and the Eugenics Society, as well as Front Line, a magazine distributed by the 1930s paramilitaristic Green Shirt social credit movement, which advocated wealth distribution by the state and used typefaces that wouldn't have looked out of place on a punk seven-inch.

Dominating the entire area is a pair of gorgeous Art Deco lifts that once belonged to Selfridges. Having ill-advisedly sold them to the museum in the 1970s, the department store promptly attempted to purchase them back – clearly to no avail.

The final gallery, World City (1950 to today), lacks any item quite as impressive, instead offering creeping nostalgia with cases crammed with books, magazines, clothes, mobile phones, LP covers and badges, with no attempt at any unifying theme. The recent past is always the hardest to get a handle on, but it would be nice to see more made of the best item, The Ghetto, a stunningly detailed cardboard model of three squatted Hackney streets made in 1994 by Tom Hunter and James McKinnon. Now stuck in a corner, it threatens to go unnoticed.

The theme of a London subdued by recession is perhaps something for the gallery to explore in future, when the purse strings might be looser and refurbishment is back on the menu. For now, though, this imaginative renovation will more than suffice.

Galleries of Modern London (020-7001 9844) open 28 May. Admission free