In his autobiography, Jeremy Isaacs describes how he bumped into Tony Essex, one of the producers behind the 1964 BBC documentary series The Great War, and asked how he did it. "At all costs, make your mind up what you are going to do, and stick with it. If you change your mind halfway, the result will be chaos", he said.

It was a lesson that stood Isaacs in good stead when he made The World at War, and one that Michael Burleigh would have done well to heed when writing Moral Combat. The result is not chaos, but it is a missed opportunity. Burleigh could have produced the best single-volume history of the Second World War. This isn't it.

Burleigh is one of the most acclaimed histo­rians of his generation. Beginning in the late 1980s, he wrote and edited a series of books on Nazi Germany, focusing largely on what he called the "racial state" and culminating in his best-known book, The Third Reich (2000). Its success allowed Burleigh to leave academia and become a freelance writer. This coincided with a turn in his work: a two-volume study of religion and politics in Europe from the French Revolution to al-Qaeda, followed by Blood and Rage, a cultural history of terrorism. In Moral Combat, he returns to the mid-20th century.

The book has all Burleigh's familiar strengths. His prose is limpid and elegant. "At official dinners," he writes of the Nazi Hans Frank, "the sweat on his face resembled a mask of cellophane, wrapping a space consisting of nothing other than ambition". The casualties in the Blitz were the equivalent, he notes, of "a 9/11 once a month for a year".

He does not pull his punches, but at times he sounds more like a tabloid journalist than the Oxford don he once was: Neville Chamberlain's response to the Anschluss was "pathetic"; Lord Halifax was a man stuck "in arrested adolescence". Defending Winston Churchill, Burleigh asserts that "wars are not conducted according to the desiccated deliberations of a philosophy seminar full of purse-lipped old maids".

Burleigh covers a vast amount of territory here: from appeasement to the Nuremberg Trials, from the Battle of the Atlantic to the conflict in the Pacific. This is a global account of a world at war. He carries his learning lightly, too, telling vivid stories retrieved from obscure academic articles. In his chapter on the Einsatzgruppen, the mobile killing units deployed by the Nazis during their invasion of the Soviet Union, Burleigh recounts how one SS regiment turned up in the town of Motol (in what is now Belarus) and killed 800 male Jews: some of them having had their hiding places betrayed by Christian children to whom the SS cavalrymen gave sweets. After a night's rest, the SS turned their attention to the women and children. They were marched out of town, ordered to undress and then mowed down with machine-guns hidden in bushes.

They returned to the town to kill any survivors, "but not before sitting down to lunch". Burleigh has an acute eye for telling detail. Among the most powerful contemporary pol­emics against appeasement was Guilty Men (one of whose authors was Michael Foot). The authors' agent, he notes, "absconded with the royalties". Discussing the failure to purge postwar Italy of Fascists, he writes that in Naples "only 23 former Fascists were fired from a public sector that employed 128,837 officials". This is outstanding history.

Yet Burleigh is at his best when he moves to the big picture. His comparison of the Nazi and Stalinist states is illuminating. And the book takes off after Operation Barbarossa, when we get to the great moral issues. Did the Allies do enough to help the Jews of eastern Europe? What motivated the extermination squads on the Russian front? And what of the charges against those responsible for Allied bombing raids? Were the raids on Dresden and Hiroshima war crimes, equivalent to Ausch­witz or Katyn?

These are hugely difficult questions, and Burleigh's tone is humane and thoughtful throughout. For example, the question of why the Allies did not do more to help the Jews is a historical minefield, and he takes us through the answers carefully and with great sensitivity. But he never sits on the fence.

There are two grave problems with Moral Combat, however. The first is the way Burleigh has arranged his material. There are two very different books here. The first half is an interesting but not terribly original account of the Second World War, from appeasement to the German invasion of the Soviet Union . Many of the best-known stories are here: Munich, the invasion of Poland , the Battle of Britain, Barbarossa, resistance and life in Nazi-occupied Europe . There are numerous interesting observations and facts, but it all feels very familiar. Burleigh's account of appeasement, for example, is one-dimensional. Norman Stone once wrote that the Czechs were betrayed by the Allies, but Prague survived intact; the Poles were helped by the Allies, but lost six million citizens and saw Warsaw destroyed. Which was the worse betrayal?

By contrast, the second half of the book is outstanding. Comprising essays on the realities of command and combat, it includes three chapters on the Holocaust, one on those who rescued Jewish victims, and two on the ethics of the Allied bombing. Burleigh's approach is thematic rather than chronological. He moves between historical narrative and the big moral questions. If the first half had been like this, Moral Combat would have been a masterpiece.

The second serious criticism concerns what is missing. Burleigh has devoured much of the scholarly literature in English and German, though there are a few surprising absences: Omer Bartov, Christopher Browning (who makes the footnotes but not the bibliography) and Richard Evans's Third Reich trilogy. But the biggest omission is the growing literature on southern and eastern Europe. Mark Mazower's recent Hitler's Empire, for instance, refers to more than 60 books and articles on eastern Europe from the past decade alone. Only two of these make it into Burleigh's bibliography.

As is the case with most accounts of the Second World War in English, Burleigh's history focuses on western Europe, Japan and the Eastern Front. The chapter on Nazi-occupied Europe concentrates mostly on France. There is no treatment of life under the Nazis in the Balkans or further east. The chapter "The Resistance" discusses only France. There is a single paragraph on the Polish home army, and the index contains two references to Hungary, three to Slovakia and one to Bulgaria.

We are still waiting for a history of the Second World War that looks at the whole of Europe, one that moves on from appeasement and the Blitz and manages to encompass economic and social history, together with the more familiar stories of extermination squads and great battles. There is much to commend in Burleigh's book, but on its own it is not enough.

Moral Combat: a History of World War II
Michael Burleigh
HarperPress, 672pp, £30

David Herman is a former television producer