More than half a century ago an African was arrested by Kenya's colonial police; he was imprisoned, tortured, and finally released two years later, a broken man. Such episodes were grimly common during the Mau Mau rebellion against British rule in Kenya, yet this sharp little shard of history has now poked above the surface again, as the story of Barack Obama's grandfather.

This is more than simply another fascinating element in Mr Obama's already colourful story. No president of modern times is so steeped in history, both America's history and his own family narrative. The past, and where he came from - Hawaii, Indonesia, Kenya, Chicago - is how Mr Obama has chosen to define himself to the American electorate.

But the story of his grandfather's treatment at the hands of the British illustrates how little we, as a country, yet know about Mr Obama's view of Britain, and the extent to which those attitudes are likely to be filtered through the prism of the past.

Recent presidents have come to office wearing the special relationship on their sleeves. George W. Bush's Anglophilia was of a familiar Republican sort, based on the belief, inherited from a father who had fought alongside the British in the war, that when the chips are down only one ally can be firmly relied on. Churchill's bust stared out from the corner of the Oval Office. When I interviewed Mr Bush, he spoke for ten, eloquent minutes about the beauty of the Scottish landscape.

Times Archive, 1952: Politics and terrorism in Kenya

The Mau Mau aims are clear enough: to foster trouble at all levels and by all means

• Archive Topic: The Mau-Mau revolt

Bill Clinton's affection for Britain was equally profound, though less emotional, reinforced by his time as a Rhodes scholar in Oxford. He could speak the language of Third Way Blairism without a trace of an accent. When Ronald Reagan told Parliament in 1982 that he felt “a moment of kinship and homecoming in these hallowed halls”, he spoke for most postwar presidents, and most Americans.

Mr Obama's relationship with Britain will also be special, but perhaps not in the ways we have come to expect. “We've been through two world wars together,” he said, on his brief visit to Britain last July - the required historical mantra. That heritage, however, may be less personally relevant than another war fought in the jungles of Kenya, in which Britain was not an ally of Mr Obama's family, but an enemy.

The experience of a grandfather he never knew, long before he was born, will not provoke some knee-jerk anti-British attitude on the part of the new president. Mr Obama is too supple a politician for that. Yet international relationships are based on emotions as well as politics, and the set of preconceptions about Britain that Mr Obama brings to the White House will be far removed from those we have become used to over the Past half-century.

Mr Obama's diplomatic remarks about Britain have been pallid and tactful; it is the more unguarded corners of his writing that offer revealing flickers of another attitude. In his memoir Dreams from My Father Obama devotes just six words to describing his first visit to Britain: “I took tea by the Thames.” The British passengers on the plane wear “ill-fitting blazers”; the one sitting next to him, an acne-ridden Mancunian, he finds aggravatingly superior, referring to the “Godforsaken countries” of Africa.

On safari in Kenya, he talks to an English doctor with “pasty blond hair” who has quit Britain to live in Africa. “England seems terribly cramped,” the man says. “The British have so much more, but seem to enjoy it less.”

These are small indications, but together they begin to form a caricature: Britain ill-dressed, pasty-faced and racially arrogant, cramped, spotty and joyless. In one of the most revealing passages, Mr Obama describes how travelling in Europe makes him feel “edgy, defensive, hesitant”. “It wasn't that Europe wasn't beautiful,” he writes. “It just wasn't mine.” So far from coming home to Britain, like Reagan, Mr Obama has described just how far from home he feels here.

Later, in Kenya, riding the imperial-era railway, he imagines “some nameless British officer”, puffed with colonial hubris: “Would he have felt a sense of triumph, a confidence that the guiding light of Western civilisation had finally penetrated the African darkness?” He squirms at the African waiters' cringing attitude towards whites in the Nairobi hotels, and mocks the tourists pretending to be characters in some imagined re-creation of Out of Africa.

The discovery that Mr Obama's grandfather was active in opposing colonial rule, and brutally treated as a consequence, will only increase the future president's cachet among black Americans. One of the few criticisms of Mr Obama in the black community was, that as an African American, as distinct from an African-American, he did not share the same racial historical scars. Yet here is evidence that his ancestor fought for racial justice, and bore the scars for the rest of his life.

Mr Obama's different historical legacy will not mean a change of foreign policy, but it may well presage a change of tone - on Guantánamo as well as Britain. For British diplomats, reading President Obama will require a new vocabulary, and understanding a different sort of history. Not the glory of shared victory over evil in the Second World War, but the more complicated history of decolonisation, in which Britain's role was sometimes less than glorious and both sides committed horrific atrocities.

Mr Obama has written movingly about how his African past has defined him; that past, still emerging, may also help to define the future of the Anglo-American relationship.

When he hears an English accent, I suspect, the new president will not automatically think of Churchill, Benny Hill or Princess Diana, but rather of some nameless British colonial officer, gazing out on an Africa he believed he owned: for that is where Obama is coming from.

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