Peter Clarke's history of 20th-century Britain is one of the first two volumes to be published in David Cannadine's new Penguin History of Britain. It is self-consciously a history of Britain (or more properly perhaps the British Isles), to make up for the missing geographical dimension in the Pelican History of England, which this series now supersedes. Its nine volumes will cover the history of the region from 100AD to 1990 in chronological spans that get progressively shorter as the modern age arrives. Clarke gets 90 years, although it must surely be irresistible to produce at some point a millennium edition that takes the story through the century as a whole.

Clarke's volume is a triumphant example of popular academic history. Its prose is clear and uncluttered and it has an extraordinary range, something for everybody. Above all Clarke is determined that his history should not be seen as the familiar tale of decline and fall. The temptation is overwhelming to see the 20th century as the age in which wrong decisions, missed opportunities, or moral uncertainty hastened the collapse of the British Empire and of the "workshop of the world". Clarke's approach is sensibly relativist. (Most) Britons live longer, eat better, earn more; they are better educated, travel more widely, enjoy the fruits of modern consumerism. Few would want to return to an age which has become easy to sentimentalise in the Merchant-Ivory way, but where there were no antibiotics, poor contraception, minimal welfare, male-only suffrage and widespread and unquestioned racism.

Clarke is aware that the decline of Britain is largely an optical illusion. Britain does play a much smaller part in the world economy - though larger today than its mere size and economic performance might have justified - and is manifestly not up to superpower status, but in all those "other histories", with which his book is richly supplied, there is little but secular improvement. The text is a mixture of political and diplomatic narrative, spliced together with brief analytical vignettes on culture, social change, and economic development - a study of Shaw and Wells before 1914, the post-1945 British cinema, youth culture, family life, and so on. This format works remarkably well, given the severe limitation of space, and the difficulty of treating social and cultural issues in anything but the long run. At times the chapters start to read like a series of essays, loosely hung together, but Clarke supplies a flexible enough framework for this not to matter. The sense of continuity is cleverly sustained despite the abrupt changes of pace and subject.

Nevertheless this is necessarily a feat of compression and selection. The focus is very much on British society and politics. The outside world is never very far away, but it is kept at arm's length. The early chapters, the best in the book, are in their way a reminder of just how insular Britain was, even when fighting the first world war. This is all the more paradoxical given the fact that Britain's elite was almost certainly more cosmopolitan than its European counterparts and has remained so, and given Britain's very high dependence until the 1970s on the wider world economy of which she had once been the prime architect.

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The insularity is perhaps unconsciously suggested in Clarke's treatment of the second world war, where the home front is much more effectively discussed than the war effort, or in the treatment of the student revolt of the 1960s, which is portrayed here as an alien import, a pale reflection of the serious business of student revolution elsewhere. There is no mention here of a quite remarkable level of violence that erupted between police and the radical student body in the late 1960s and 1970s, remarkable that is in the context of a civil sphere where violent confrontation had almost died away from the Fascist/Communist fights of the 1930s.

No doubt the many veterans of the Grosvenor Square demonstrations (not mentioned here) have all gone off to become lawyers and teachers and accountants (I have to admit sheepishly to being present on both occasions), but the police and security forces used the three or four years of violence to begin a programme of riot rearmament and retraining that transformed the Dixon of Dock Green image of the 1950s.

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It is all too easy of course to point to omissions and understatements in what is a vastly complex story, told throughout with nice attention to detail and a light humour. But on the wider issues of Britain's century there remains, as Clarke no doubt intended, a good deal of room for interpretation and argument. Take, for example, the part played by the two world wars in shaping Britain's international role and home affairs. The wars themselves get relatively short shrift - the whole of the crisis from 1937 to 1945 is contained in only 30 pages - and as a result a great many issues of real substance are glossed over. The section is unhappily littered with small mistakes, which mar what is in general a scrupulous text (the Polish guarantee was Chamberlain's idea, not a consequence of Polish importuning; radar covered much more than Britain's "eastern flank"; Britain's combat dead totalled 1,000, not 360,000: counting empire dead the figure is 395,000; Rommel did not replace, but supplemented Italian forces in 1942; and so on).

The treatment of British strategic bombing is strikingly superficial. It was not Harris who was the principal influence on Churchill to pursue a bombing strategy, but Cherwell and Portal, before Harris was even appointed. Dresden was not the culmination of bombing strategy, but a byproduct of the final stages of the land war. What we do not get here, and it is surely a critical question, is why the society Clarke describes with all its liberal credentials should embark on a strategy that killed more than 400,000 German civilians, and is now widely (in my view wrongly) discussed as an example of 20th- century genocide. Bombing was like nothing else the British did, save perhaps the naval blockade of the first world war. It raises all kind of awkward issues about democratic violence which have rumbled on in popular debate down to the Gulf war.

Clarke's treatment of class conflict is another area where the passion and violence has somehow been squeezed out. In the 1970s and 1980s class tensions led, late in the day, to a high level of violence and tension immortalised in the photographic record of the last great miners' strike in 1984. The collapse of the old working class and the industries that sustained them is a very large story, and it deserves more. Clarke's discussion of class - a concept now regarded by many as a conceptual dinosaur - is unfortunately shot through with an uncharacteristic snobbishness about "shell-suits, rottweilers, lager and Murdoch's Sun". There is an obvious rejoinder - Volvo estates? Australian Chardonnay? gte holidays? Marks and Spencer pullovers? This rings bells too, but does it tell us anything other than the depressing truth that a century of social improvement and labour mobility has left Britain as riddled with class prejudice as it always was? Roll on, European Union.

These are small blemishes on what is otherwise an important summing up. The great strengths of the book - its dry wit, its judiciousness, its lack of undirected passion, its constant good sense - make it a very British (dare one say English) product. Clarke stands firmly in the tradition of Taylor and Trevelyan; we will still be reading him years hence.

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Richard Overy is professor of modern history, King's College, London.