"The only working-class people who still have well-paid jobs in London are his members," commented Ken Livingstone after the recent death of the RMT's Bob Crow – a moment that in itself seemed to have a particular resonance, as one of the few major and unashamedly working-class presences in public life suddenly left the scene.

The timing is apt for Selina Todd's examination of what she calls "the rise and fall" of the working class. Inequality of outcome remains gapingly wide, Ukip palpably feed off "left behind" working-class disenchantment with the established political elite, and the head of policy at the Social Mobility and Child Poverty Commission wants working-class children to behave more like middle-class children in order to increase their currently slender chances of getting into the best universities.

There is a longer shadow, though, lurking behind this book: EP Thompson's The Making of the English Working Class. Published in 1963, and demanding an end to "the enormous condescension of posterity" towards the working class, it became an almost instant classic and over the next two decades exercised huge sway over younger historians. But then things changed. Just as the defeat of the miners in 1985 conclusively crushed the politics of class, leaving the Labour party without a clear purpose, so historians turned increasingly to the more individualistic politics of identity, above all those of gender and ethnicity – to the despair of at least one historian, Tony Judt, trained in the old progressive verities. Suddenly class seemed irrelevant, sociology and economic history departments struggled to attract students, and cultural studies boomed.

Put another way, The People is a book we badly need. It is also a book the author badly needed to write. The 2000s saw two notable if smaller-scale histories-cum-memoirs by working-class writers – The Likes of Us by Michael Collins and Estates by Lynsey Hanley – and now in 2014 this is similarly fuelled by a personal working-class background. "I looked in vain for my family's story when I went to university to read history," relates Todd (born in 1975), "and continued to search for it fruitlessly throughout the next decade. Eventually I realised that I would have to write this history myself."

To a large extent she succeeds. The People offers a clear, compelling, broadly persuasive narrative of a century of British history as seen through working-class eyes and from a working-class perspective. Todd avoids hectoring, but by the end one is left suitably angry: the people have been screwed.

"Servants", the first of her three parts, covers 1910-39 and shows how the numerically overwhelming working class began at last to move towards the centre of the national stage. She brings out the continuing importance of domestic service (a world of petty indignities and self-deluding paternalism), charts the upsurge of industrial militancy that culminated in the General Strike of 1926 (a serio-comic chapter called "Enemies Within", with Winston Churchill as main villain), and evokes the misery of mass unemployment during the 1930s, a misery seriously compounded by the punitive approach of the National government – in effect the Conservative government – to those on the dole. "The Jarrow marchers of 1936 would eventually be commemorated for having helped to shape a national debate about unemployment and the causes of poverty," reflects Todd movingly. "But that unknown future could not compensate them for returning home workless and hungry, in the knowledge that their prime minister [Stanley Baldwin] refused to see them."

The second part, "The People", traces what were, relatively speaking, the glory years, 1939-66: how during those middle decades the second world war changed the terms of trade between the middle and working classes, the postwar Labour government not only created the modern welfare state but to a significant degree redistributed wealth, and full employment through the 1950s and into the 1960s ensured a not wholly lopsided balance between employers and their workforces. Todd's treatment of the immediate postwar years is particularly striking: austerity Britain, yes, but a time of real hope and expectation for many working-class people who had had far grimmer experiences during the interwar years.

The final part, "The Dispossessed", starts in 1966 with a Labour government elected with a thumping majority – the only time between 1945 and 1997 – and has an insistent note of disappointment, even bitterness. Harold Wilson no longer on a crusade to end social inequality; the justified attempt by organised labour to level the industrial playing field trumped in the 1970s by "the calculated strategy of those bankers, financiers and rightwing politicians who controlled the IMF, and which provoked a global free market at the expense of workers' welfare"; Margaret Thatcher, far from trying to restore full employment, using unemployment as a brutal stick with which to destroy the power of the trade unions; New Labour a middle-class coup with no roots in the working class; and by 2010, a working class in post-industrial Britain that had been thoroughly marginalised and even demonised.

Todd may have a palpable design on us, but she is a subtle as well as powerful historian. Retrospective oral testimony can be a problematic type of source, but she uses it with a dexterity and intelligence comparable to Orlando Figes in his masterly The Whisperers; weaving through her account the rollercoaster life story of the celebrated pools-winner Vivian Nicholson ("spend, spend, spend") works beautifully; above all, she has an enviably assured grasp of the realities at any one time of working-class life. She shows, for instance, how the so-called "affluent worker" of the 1960s was far from a myth, but that the price that had to be paid for that relative prosperity was massive quantities of overtime and severe strain on family life.

Or take the ever-thorny, still emotive question of social mobility during the 1950s heyday of the grammar school. The conventional wisdom among most contemporary observers, subsequently accepted by historians, was that working-class parents were principally to blame for the disappointing educational attainment of their children; but, argues Todd, that moralistic censure entirely failed to take into account that most parents had known the desperation of trying to get work and to make ends meet – and now, in easier, more certain times, what they most wanted was for their children to be happy and secure, as opposed to passing exams and being upwardly mobile. It is, at the least, a salutary interpretation.

Any survey is of course open to criticism. Todd's treatment of working-class culture is deliberately restricted, but it still seems strange to have nothing on football, arguably the ultimate case in recent decades of working-class dispossession; nor does she quite confront head-on the vexed issue – myth or reality? – of traditional working-class "community" before the slum clearances of the 1960s (themselves rather skimpily covered) physically tore asunder where much of the urban working class had lived.

There is a more fundamental point to be made. Todd rightly concedes the existence of a significant individualistic strain within the working class, even at its mid-century collectivist height; but what she is less willing to contemplate is that that strain became sufficiently strong that in the fullness of time the working class as a whole was not only a victim of what for shorthand we call Thatcherism, but also an agent of it.

That, though, is at the level of causation. The underlying truth of the story – ultimately a tragic as well as a shocking story – that Todd tells remains essentially valid. And she tells it in a way that is, as Henry James might have said, the real thing.