At first glance, it seems remarkable, reading this behind-the-scenes tour of high-level policymaking in the second world war, that the allies managed to defeat the Germans at all. The British foreign secretary was sedating himself with cocaine, while Alan Brooke, the highly strung chief of the imperial general staff, distracted himself from the torments of working with his prime minister by heading off bird-watching and fishing as often as he could, and burying himself in ornithology books (from Audubon to The Truth About the Cuckoo ) when he had to be in London. Winston Churchill, decked out in his pale blue "romper suit", his black silk dressing gown with the Chinese dragons or (as sometimes happened) wearing nothing at all, veered between moments of extraordinary strategic insight and sheer petulance. Meanwhile, split by deep inter-service rivalries, the American high command was hamstrung by the court politics of the White House; indeed, General Marshall - Brooke's US equivalent - often needed sympathetic Brits to tell him what his own president was thinking.

Andrew Roberts's book adds relatively little to our knowledge of the evolution of allied strategy during the war: the tussle between London and Washington over when to open a second front in France, the American reluctance to consider a north African landing, and their even greater reluctance to go on into Italy for fear of being led "down the garden path" by the deviously imperialist British. But by mining previously unavailable diaries and oral histories - a surprising number of senior policymakers were ignoring the rules and jotting things down at night - this book brings vividly to life the personal interactions and impressions of those involved. Roberts has a keen eye for the telling anecdote, and he gives a vivid sense of the extreme strains generated by a struggle fought not in the field but in committee rooms and offices.

If personality still unquestionably mattered in the age of industrial warfare, one is nonetheless aware of those military-industrial complexes grinding inexorably away. As rearmament got into gear on the other side of the Atlantic, the balance of power between London and Washington swung to the latter. Nor was either unaware of the two other war machines, Nazi Germany and the USSR, locked in their mortal struggle in the east, a struggle that, as Roberts himself notes, was really where the overall outcome was decided.

The crucial thing was that the British and the Americans had been able to agree on the fundamentals from a very early date: Germany and victory in Europe first, Japan second. Britain was to be the launchpad for a second front that would help the embattled Soviets and lead to the downfall of the Third Reich. But that still left plenty of room for disagreement: over timing, the scale and distribution of commitments, and whether or not there was any need for sideshows before the big showdown in France. Both sides were prepared to make serious concessions. But both also had deep misgivings about their partners. Brooke thought the Americans lacked any real strategic sense and underestimated the difficulties of a cross-Channel invasion. Marshall suspected that the British cared more about shoring up their empire outside Europe than taking on the Germans inside it. Roberts describes both men with evident admiration as gentlemen - Marshall is "steely", Brooke "flinty" - able to work with one another despite their differences. But when it came to compromise, both of them needed their political leaders. One of the things that prevented the alliance from falling apart early on, when things were hardest, was Roosevelt's willingness to back Churchill against his own chiefs of staff: this was the precondition for the decision to invade north Africa in 1942. The following year, it was Churchill who gave ground when he accepted that the Americans would allow an invasion of Italy only if he committed himself to a landing in France in 1944.

In other words, led from the top by the mutual trust of two men who scarcely knew each other before the war, the two Atlantic powers quickly established a remarkably close understanding. What is really striking is not that there were differences or strains between the allies, but that their partnership worked so well. One shudders to think how the war might have gone had the Germans been half as cooperative with their allies. But there was no special relationship between Berlin and Tokyo: if there had been, the British might have been in serious trouble, and the Russians too. Nor was the German interaction with the Italians any better, despite the fact that as fellow fascist powers they were actually fighting alongside one another in the Balkans, Ukraine and north Africa. Neither Mussolini nor Hitler was capable of trusting the other, even though (or was it because?) by 1939 they had known each other far longer, and better, than Churchill and Roosevelt. In fact, not only was Hitler congenitally incapable of taking alliances seriously; he even made sure he sabotaged the kind of consultative policymaking that was ingrained in Whitehall and emerged during the war in Washington as well. Deliberately isolated in his east Prussian headquarters, the Fuhrer seemed determined to run the war alone, to the despair of his Berlin-based civil servants who faced the unenviable choice between staying in their ministries and losing the Fuhrer's ear, or hanging round damp eastern estates on the off-chance of being granted an audience.

One of the fascinating insights offered by Roberts is that Hitler's high estimation of his own men's fighting qualities was entirely shared by the British. Brooke had seen what the Wehrmacht could do in France in 1940, and he was worried. In fact, he was convinced that the Americans' lack of experience with the Germans - incredibly, Marshall had never commanded in the field - led them to underestimate the difficulties involved in taking them on. He was terrified that a poorly prepared invasion could lead to disaster, or even, Churchill warned at one point, to the loss of the war itself. This nervousness about how British troops would perform in an even fight with the Germans was one of the main reasons for Brooke's refusal to go into France before 1944; and it raises interesting questions about whether this patrician wartime elite, presented so positively by Roberts, was not in fact rather more nervous about British morale and social cohesion than their German counterparts.

Away from the field, both Brooke and Marshall liked to prepare their ground carefully. In fact, Masters and Commanders can be read as a guide to the art of warfare by committee, something in which the British for a long time enjoyed an advantage over the Americans. It took a while for them to wise up, and through 1942 and early 1943, the strategic arguments tended to go Whitehall's way. But whether or not Marshall was as poor a strategist as the acidic Brooke believed - he rated only Stalin, Jan Smuts and General MacArthur highly - he was a brilliant organiser, and the Casablanca meeting, held at the start of 1943 in a Moroccan seaside resort stuffed with French pornography and other distractions, was the last at which the British came out ahead. Even before the D-Day landings, it was obvious that the British were now the junior partners.

Was the alliance's victory the result of luck? Or did it reflect the superior strategic wisdom of the democratic way of waging war and of making grand strategy? A bit of both, perhaps. It was basically luck that when the British could make their wishes prevail, they were probably right on the big questions - the peripheral strategy of going into the Mediterranean was a much better idea than attacking France before 1944 - and that when the Americans won out, in 1944, they were right, too. But Roberts also suggests that making strategy by open argument through committees worked, and that this averted or minimised the impact of some of the crazier ideas that Churchill and Roosevelt were prone to pushing. It was to their credit that they realised the benefits of surrounding themselves with independent-minded advisers who would stand up to them. And Marshall and Brooke, men of virtue both, sacrificed opportunities for battlefield command and glory in order to keep their political masters in line. But neither virtue nor democracy is necessary in war, and over in Moscow another master and his commanders were taking the decisions that counted.

 Mark Mazower's Hitler's Empire: Nazi Rule in Occupied Europe is published by Allen Lane.