Who were the most important American and British military commanders during the second world war?

Well, my guess is that most people would say General Dwight Eisenhower on the American side, and Field Marshal Bernard Montgomery on the British side. They are certainly the most famous. But, as Andrew Roberts shows us in Masters and Commanders, they were not the most important. It was Field Marshal Sir Alan Brooke (later Lord Alanbrooke) in London, and General George Marshall in Washington, who, along with their political masters, Winston Churchill and Franklin D Roosevelt, determined the strategy that the West needed in order to fight the war.

Roosevelt and Churchill were both tough egomaniacs, and Brooke and Marshall had to be equally tough — if not equally as egomaniacal — in order to work closely with them. Roberts, with considerable panache, charts the story of how these military men tried to handle their bosses. He is helped, of course, by the fact that Churchill was not just a human being; he was also a force of nature.

Brooke revealed in a letter to General Wavell just how exasperating it could be, dealing with the British prime minister: “If I were to take offence when abused by Winston and given to understand that he had no confidence in me, I should have to resign at least once every day!” But the reality was that Churchill was mostly big enough to take criticism from Brooke, even if on at least one occasion it all got too much for him. “I have decided to get rid of Brooke,” Churchill told General Ismay after one particularly fractious meeting towards the end of the war. “He hates me. You can see the hate in his eyes.” It was only after it was reported back to Churchill that Brooke had said in response that, “I don’t hate: I adore him tremendously; I do love him, but the day that I say that I agree with him when I don’t, is the day he must get rid of me because I am no use to him,” that the bitter quarrel was diffused.

As for Marshall, he had to deal with a different problem — a president who wouldn’t tell him all that was going on. Roosevelt deliberately ran a White House with a disorganised command structure — he once said he didn’t like to let his “left hand know” what his “right hand was doing”. This meant that “half the time” Roosevelt didn’t show Marshall the messages he was sending the British. The only way Marshall could find out what was happening was to talk in secret to Sir John Dill, Churchill’s representative in Washington. “I had to be careful,” Marshall later said, “that nobody knew this . . . because Dill would be destroyed in a minute if this was discovered.”

Roberts, with the help of access to a little-used source — Lawrence Burgis’s verbatim reports of the British war cabinet meetings — also demonstrates in exacting detail the extent to which there were quarrels between the two countries. The picture he paints of the relationship between the British and Americans is a long way from the cosy propaganda of the “special relationship”.

In fact, the two countries disagreed for months over one key strategic question — the proposed date of D-day. Although there were many turns in the argument, the essential difference was that the Americans, and in particular Marshall, wanted to mount a cross-channel invasion much earlier than the British had in mind. In the end, the British got their way, and D-day — as everyone knows — was not launched until June 1944.

What is much less well known is that Roosevelt, at a vital meeting held at the White House in May 1942 with Molotov, the Soviet foreign minister, all but assured the Soviets that an invasion of France would take place that very same year — that is to say two years before it actually did. Roberts describes Roosevelt’s statement as “reprehensible”; and he is right. Roosevelt’s apparent assurance to the Soviets that a cross- channel operation would take place in 1942 was a huge blunder. It caused immense problems for the alliance later on, not least because it meant that Stalin felt betrayed when the invasion was not launched until 1944.

The Soviet leader was desperate for this “second front” to be opened as soon as possible, because it would take the pressure off the Red Army, which was fighting a brutal series of battles against the Germans on Soviet territory. Stalin, already suspicious to the point of paranoia about western intentions towards the Soviet Union, was thus given a ready-made reason to distrust the Americans (and by association the British). This failure to deliver, on what the Soviets believed was a firm promise to help, cast a long shadow.

All of which makes it ironic that Brooke — who had argued vigorously against the second front happening as early as the Americans wanted it — was so excited when he was told by Churchill in June 1943 that he would “take the Supreme Command of operations from this country across the Channel when the time was suitable”. Brooke recorded later that he felt “it would be the perfect climax to all my struggles . . . to find myself ultimately in command of the allied forces destined for this liberation!”

But Churchill couldn’t deliver on this offer — two months later he brusquely told Brooke that the job had to go to an American. And just as Churchill disappointed Brooke, so Roosevelt disappointed Marshall. The job of supreme allied commander at the time of D-day finally went to Eisenhower. As a result, neither the name of Brooke nor of Marshall has entered the public consciousness as it should.

In Masters and Commanders, Roberts offers us a compelling analysis of American and British military strategy during the war. He also tells a profoundly human story — of two soldiers who loyally served their masters, only to be each denied at the end the prize that would have made one of them world famous.

Times Recommends

• The 100 Best Books of the Decade
• The Times picks the 50 best paperbacks of 2009
• The conversation: James Ellroy