Just who are the people whom a "people's history" of London might commemorate? Since the late 1930s the "average" Londoner has been a woman, working at home or at a factory bench or shop counter or office desk and living in the suburbs. She hardly gets a look-in here. Nor do the semi-skilled workshop "hands", the uniformed railway or postal workers, or the myriad low-paid black-coated clerks of the London of Queen Victoria's diamond jubilee. We are living through a genealogical epidemic, where family historians search for ancestors in Newgate or the workhouse or the first transport to Australia; but their narratives of unsteady upward social climbing through the many ranks of Londoner  sometimes slithering downwards along the way  are not the stuff of this "people's history".

The "people" here are pretty much how Lindsey German and John Rees might well have chosen to cast their own metropolitan ancestors had genealogy dealt them a free hand. This is a history of London radicalism from the perspective of two self-proclaimed activists desiring to construct an alternative lineage as unimpeachable as the Duke of Westminster's. And for all the pitfalls and difficulties, not all avoided, it acquits itself admirably.

It's necessarily a book of ambitious scope. Rebellion does indeed have a long history in London. Inevitably, this early history of radical London is much foreshortened within the context of the book as a whole. The first 1,700 years of London's history are telescoped into just over 50 pages, while the last 200 years get something like a page each. In between is the turbulent 18th century, where there are useful summaries of the Spitalfields weavers' disputes of the 1760s, the constitutional upset caused by "that devil" John Wilkes, and the Gordon riots of 1780. These are all episodes teeming with action and drama that are difficult to summarise in a coherent way, but the authors do the job with verve, while still finding space for insightful analysis.

With the 19th and 20th centuries, the terrain gets more crowded and the pace quickens. There really is so much to tell. We are given the Cato Street conspiracy of 1820, the turmoil over Queen Caroline, Chartism and the revolutionary moment of 10 April 1848, at least as it appeared to the anxious metropolitan middle classes, who armed themselves with bludgeons and shooters to keep London's workers at bay. Quick on Chartism's heels arrive Karl Marx and others of the European revolutionaries' diaspora. Then, in those most expectant years from 1887 to 1889, a new English socialist movement seemed to construct yet another revolutionary opportunity with Bloody Sunday in Trafalgar Square, rioting by the unemployed, and the memorable and influential strikes by East End match-makers, gas workers and dock labourers.

From then on the pace of radical activity in London seems hardly to abate. Suffragettes, Russian anarchists and revolutionary appropriators, and a host of striking unionised transport workers harry the ruling classes of Edwardian London. Munition workers' strikes in the first world war, the rebellion of the Poplar councillors in 1921, the general strike of 1926, the Great Depression with its hunger marches and riots of the unemployed, the Battle of Cable Street, East End rent strikes, and the strike by busmen that cocked a snook at Coronation Day, 1937, are all charted with vigour. And within the reach of popular memory is the long litany of struggle in our own time: CND, student unrest, the Winter of Discontent, Grunwick's, rate-capping, Fortress Wapping, the poll tax, anti-war demonstrations, right up to the August riots of 2011. The list is not exhaustive, but it certainly is exhausting. It makes one wonder how so many Londoners in these same years found time to live and love, hold down a job and fund a mortgage, but maybe they aren't "the people" whose history is narrated here.

For when all is said and done, this is a very selective people's history. There are different, perhaps larger histories to tell. The first world war and the interwar period, for instance, were for most Londoners years of unprecedented prosperity. They saw the end at last of those 19th-century depths of poverty that continued to blight the lives of the metropolitan working class till 1914. It was largely London and its new manufacturing industries, in what some thought of as the second industrial revolution, that dragged Britain out of the depression of 1929-32. And they were years that saw London double in size on the ground and reach its greatest population number  around 8.6 million, a million or so more than the present day.

It's selective in other ways, too. It turns, for instance, a blind eye to the numerous merciless IRA bombing campaigns in which so many Londoners suffered, and suffer still. And it stays silent about 7 July 2005 while choosing to commemorate "an iftar or breaking of the fast" involving Muslims and others in November 2001. It's when dealing with these later events that the choice of subject matter as well as the stridency of the writing becomes unhinged, fitting uneasily with the more balanced approach of the earlier chapters. No shade of grey is admitted in a narrative where all rioters are incipient revolutionaries and all coppers are bastards.

The publishers hail this book as the "forgotten history of London, the world capital of revolution". In fact, it is all pretty familiar to those acquainted with the many social histories of London. And "world capital of revolution" might raise eyebrows in Paris or St Petersburg. Even so, when the evidence of London's diverse radical traditions is brought together in one place, as here, it truly does tell an impressive story. And in a city where the past weighs unusually heavily on the present, these are traditions that nurture and sustain the rebels and radicals and protesters of today. So the Poplar councillors became a clarion call for those opposing rate-capping in the mid-1980s, and some anti-poll tax protesters a few years later saw themselves as quite consciously following in the steps of Wat Tyler and 1381. When the summer riots of 2011 broke unexpectedly on the capital, commentators sympathetic or otherwise could reach for numerous historical parallels, stretching as far back as 1780.

All these events and many more are energetically marshalled here as models of encouragement or caution. And those who continue to uphold London's living traditions of protest will be able to take heart from this fresh and welcome look at the city's history.

 Jerry White's London in the Eighteenth Century is published by Bodley Head.