Can anything new be said about the second world war? Unexpectedly the answer is yes. Here are just a few of the surprising facts that I learned from this revelatory book. The Belgian army in 1940 was twice the size of the British Expeditionary Force. (The US army in 1940 was smaller still, smaller than those of Portugal or Sweden.) Almost all the French troops evacuated at Dunkirk chose to be repatriated rather than join the Free French. In 1942 pro-Russian feeling in Britain was so strong that War and Peace became a bestseller. Even in January 1945 the Japanese still had 1 million troops in Manchuria. The Indian prophet of non-violence, Mahatma Gandhi, considered Hitler “not as bad as he is depicted”. And so on.

Tim Bouverie has reverted to a traditional form to present the past afresh. His focus is not on the battlefield, nor on the Home Front, but on the relations between the allies who opposed Hitler. In the foreground are the leaders, especially Churchill, Roosevelt and Stalin, of course; but there are also walk-on parts for the foreign ministers, the ambassadors, the emissaries and others who participated in their discussions. This is a work of old-fashioned diplomatic history, which provides new perspectives on subjects that seemed familiar. One of its merits is to present the choices that faced the allied leaders as they appeared at the time, rather than with the benefit of hindsight.

The first such alliance was between Britain and France, which declared war on Germany in September 1939 to honour their joint guarantee to Poland, though neither did much to prevent Poland from being overrun. The Anglo-French strategy was to bring Germany to its knees by means of a blockade. Fearful of reprisals, the RAF dropped leaflets rather than bombs on the enemy. The “phoney war” ended when the Germans suddenly invaded France in the spring of 1940. Churchill had expected the front to stabilise, as it had done in 1914, but instead the German Blitzkrieg split the allied armies in two. France was defeated, and Vichy France became neutral, indeed a potential enemy. Britain fought on alone against the axis powers of Germany and Italy, which had entered the war as France was collapsing. Bouverie stresses the moral authority that Britain gained from defying German hegemony, even when the struggle seemed hopeless, while not neglecting “the shame and guilt” felt by the British as they abandoned the Greeks to axis occupation. The painful decision to attack the French fleet at Mers-el-Kébir rather than allow it to fall into German hands convinced Roosevelt of Britain’s determination to continue.

Churchill knew that Germany could not be defeated without US help. Early in 1941 the American, British and Canadian staffs met to agree plans for the US to enter the war. At the outset the British found their US allies “hopelessly disorganised”, but the creation of the Combined Chiefs of Staff provided the structural basis for “the most integrated and successful military alliance in history”. In August 1941, Churchill and Roosevelt met in Newfoundland to agree an “Atlantic Charter”. Although willing to provide succour, the US president was unwilling to commit himself further. Bouverie makes the important point that in the US, unlike in Britain, elections continued throughout the war. Then as now, the US public was isolationist in mood, wary of foreign entanglements. Only in December 1941, after the surprise Japanese attack at Pearl Harbor, was the US dragged into the conflict. Hitler helpfully declared war on the US in solidarity with its Japanese allies.

By this time, Germany had invaded Russia, which became the third member of the “Grand Alliance”. The “Big Three” of Churchill, Roosevelt and Stalin met for the first time in Tehran towards the end of 1943. This conference led to some incongruous exchanges, especially in the evening. When Churchill remarked that the political complexion of the world was changing and even Britain was becoming “a trifle pinker”, Stalin rejoined that this was “a sign of good health”. The old anti-Bolshevik crusader then drank a toast to the “proletarian masses”, prompting Stalin to raise his glass “to the Conservative party”.

Churchill praised Roosevelt as “the truest friend… the greatest man I have ever known”. Nevertheless, differences between them remained, one being their contrasting attitudes to France. Churchill insisted that France should be restored to its position as a great power after the victory. He recognised from the start that Charles de Gaulle, though often exasperating, was “the man of destiny”; in contrast, the Americans continued to lend legitimacy to the collaborationist regime at Vichy until it collapsed, while treating De Gaulle and the Free French forces as “a band of nuisance rebels”. The Russians were able to exploit the divisions between the western powers. Roosevelt mistakenly believed he could handle Stalin, rather as the current president seems to believe that he can handle Putin. Sometimes he dealt with Stalin without consulting or even informing his closest ally.

The British resented US criticism of their empire. Taxed by a New York hostess about the plight of the “wretched” Indians, Churchill asked, mischievously: “To which Indians do you refer? Do you by any chance refer to the second greatest nation on Earth, which under benign and beneficent British rule has multiplied and prospered exceedingly, or do you mean the unfortunate Indians of the North American continent, which under your administration are practically extinct?” Black American GIs, who had to endure a colour bar at home, were welcomed in Britain. Bouverie quotes a West Country farmer who, on being asked what he thought of the visitors, replied that he got on very well with Americans, “but had no time for the white men they had brought with them”.

Bouverie’s commentary is fair and his judgments judicious. Though he has obviously undertaken a vast amount of research, he never becomes overwhelmed by his material. On the contrary, his book is enjoyable to read. He writes lucidly and lightens his weighty subject matter with well-chosen vignettes – for example, describing how, at a critical conference in June 1940, the British liaison officer Major-General Edward Louis Spears snapped his pencil in frustration at French expressions of defeatism.

Bouverie’s first book, Appeasing Hitler: Chamberlain, Churchill and the Road to War, published in 2019, was a dazzling debut. Allies at War fully confirms the promise shown by its predecessor.

Adam Sisman’s most recent book is The Secret Life of John le Carré (Profile)

• Allies at War: The Politics of Defeating Hitler by Tim Bouverie is published by Bodley Head (£25). To support the Guardian and Observer order your copy at guardianbookshop.com. Delivery charges may apply