In the mid-19th century, received wisdom had it that the way to ensure goodwill between nations was for their royal families to inter-marry. And so it was that at the outbreak of the first world war, the heads of state of Britain, Russia and Germany were cousins.

Germany's Kaiser Wilhelm II  Queen Victoria's first-born grandchild  was arrogant, posturing, unpredictable and, in the opinion of many who met him, mad. Throughout his life he was torn between a desperate need to be loved by Britain and a fanatical hatred of its power. Tsar Nicholas II, meanwhile, was a deeply indecisive leader, happiest at home with his family, with a court of some 16,000 people (including 200 ladies in waiting for the tsarina) insulating him from the harsh realities of his medieval empire. His detachment and lack of self-awareness meant that when in May 1896 a stampede at a feast in Khodynka to mark his coronation left thousands of his subjects dead, the tsar didn't stay at home to mourn; instead he spent the evening at a ball, and was photographed there drinking champagne.

George V was less reprehensible, but hardly a great figurehead for the largest empire on earth. A shy, dull man who had no wish to succeed his extrovert father, Edward VII, he enjoyed shooting but had painfully little interest in the outside world (Harold Nicolson, a previous biographer, wrote: "For 17 years he did nothing at all but kill animals and stick in stamps").

Miranda Carter paints a superb picture of the three cousins and their intertwining lives, from their strict, isolated and at times deeply unhappy upbringings, to the war that ended with two of them brutally deposed. As the increasing suspicions and tensions between the great powers lead to an arms race and then inexorably to war, she offers a fascinating and frequently darkly funny account of the interactions between the three  and between the monarchs and their long-suffering ministers.

Quoting extensively from their correspondence, Carter exposes Wilhelm's deep insecurities and reveals the strong friendship between George and "Nicky", which makes perhaps the most damning revelation about the British king all the more shocking. In 1917, with Nicholas having been forced to abdicate and placed under house arrest, George refused the Romanovs sanctuary in the UK, fearing their unpopularity might prove catastrophic for him.

At least George did learn from the fate of his cousins (Wilhelm had been effectively sidelined by his generals and was later exiled). He saw that for the royal family to survive it had to adapt; today's decorative, ceremonial monarchy is the legacy of that realisation.

There are times reading this book about the run-up to the first world war when you could be forgiven for thinking that you've strayed into a Gilbert and Sullivan opera, one with extra dialogue by Lewis Carroll. As Europe unravels, three royal rulers play toy soldiers with real armies, squabble over whose yacht is biggest, and write teary letters reminding each other that they are all descended from joint stock and so should really try to get along. Ruritanian touches abound. Kaiser Bill spends his evenings designing fancy new uniforms, his cousin King George pores over his enormous stamp collection, while another cousin, tiny Tsar Nicholas, rattles around his enormous palaces worrying that something important about the peasants has slipped his mind.

Meanwhile the Austro-Hungarian empire totters, the peasants are revolting and there's an anarchist on every corner. It was, of course, as a bulwark against this kind of violent fragmentation that Prince Albert had instituted the policy all those years ago of peopling the thrones of Europe with his and Victoria's descendants. Any potential aggro could be sorted out over an appeal to shared bloodlines and an invitation to come and stay for Christmas. With a dense network of sisters, cousins and aunts - all those Louises, Sophies and Alices - binding a patchwork of nations, states and principalities together, it would be a bold, and frankly rather rude, king who dared pull the trigger on his relatives.

Albert's plan didn't work, mostly because he was unable to foresee the dramatic shift in the nature of monarchy which took place during his grandchildren's lifetime. When George, William and Nicholas were born in the 1860s, kings still made things happen. They led armies, intervened in foreign policy and could, on occasions, bend domestic policy to their will. By the time these ageing young bucks came into their inheritances, the situation was changing. In ancient, constitutional Britain and young, militaristic Germany, it was now the elected politicians who had all the power. Only in Russia did things remain almost the same. Nicholas retained the powers not merely of an emperor but also a god. It was for that reason he got shot in 1918 while the kaiser, personally unpleasant but by now politically neutered, was allowed to go into exile in Holland, where he spent the rest of his life firing off enthusiastic telegrams to Hitler. George alone managed to hang on to his throne until eldest son David, aka Edward VIII, gave it away in 1936.

In her previous book, her first, Miranda Carter did a brilliant job of integrating the life of the spy and art historian Anthony Blunt into the slippery context of mid 20th-century international politics. Here, she sets herself an even bigger task, taking on the history of Europe - which in those colonial times pretty much meant the entire world - from 1860 to 1920. As a result, she is obliged to spend large stretches rehearsing grand political narratives - the Boer wars, the Winter Palace massacre, the building-up of the German navy - which at times becomes overwhelming (the book runs to almost 600 pages) and just a little dull. There is also the problem that some of these stories are already as worn as a George V penny. Being told how Princess May of Teck was obliged to turn her marriage ambitions smartish from dead Prince Eddy to his brother, or how Rasputin had to be poisoned, shot and drowned before anyone was satisfied that he was really dead is fun but familiar, sometimes wearyingly so.

Much more fresh and enjoyable is Carter's detailed account of how an already dysfunctional family turned toxic. The starting point for all the madness was Victoria's plump lap, on which a series of remarkably plain grandchildren were obliged to pose for the obligatory photograph before being dispatched back to whatever European nursery from which they hailed. From this point rivalries and envies built up as each of the 40 children tried to find their own special place in a dynasty that had never set much store by the individual. Mostly the squabbling remained infantile: Wilhelm called Nicholas a "ninny", Nicholas's sister said that the English royals smelled. Meanwhile everyone hid behind the bushes at Osborne the moment Granny Victoria wobbled into view.

All this is funny as far as it goes, but Carter reminds us that what we are watching is nothing less than the first steps towards armageddon. In the process she offers a valuable corrective to the tendency of recent years to tell history in terms of grand, impersonal forces rather than through the quirks of personality. While no one would want a return to the days when the outbreak of the first world war was routinely ascribed to the fact that Wilhelm wanted to punish the world for his withered arm, Carter's thoughtful reintroduction of the vividly human to late 19th-century international politics is timely and welcome.

 Kathryn Hughes's The Short Life and Long Times of Mrs Beeton is published by HarperPerennial. To order The Three Emperors for £23 with free UK p&p call Guardian book service on 0330 333 6846.