When Louise Michel – teacher, anarchist, and revolutionary-in-exile – arrived in London after seven years banishment in the South Pacific, she brought five cats with her. Escorted from the ship under the coats of sympathisers, the oceanian felines, exhausted from their 10,000-mile journey, recovered quickly when presented with “an enormous bowl of milk” under the doting eye of their mistress. Back in Paris a few years later – cats in tow – Michel tried to explain her solicitude for the fragile animals. Taken from New Caledonia, her place of exile, to France, the land of her birth, the cats represented to Michel something elusive, precious, instinctual; hard to find, easy to lose. They reminded her, she said, of home.

And although William Atkins’s Exiles is framed by the pain and self-discovery of exile, it’s home that draws his subjects out; raises them up; and pulls them back, in the end, to where they began. Exile isn’t, as Atkins shrewdly comments on Ovid’s poems on the theme, a place so much as a process, a movement. All three of Atkins’s subjects – Michel; Russian anthropologist Lev Shternberg, and deposed African king Dinuzulu – discover that it’s a movement that can last a whole life. As another of the book’s luminaries, Victor Hugo, notes: once an exile, always an exile. You can go back to the place you started from. But you can never go home.

In a restless, rootless world, the idea of exile has broad purchase. Atkins taps into this, judiciously mixing history with memoir: at the time he’s researching the book, travelling from Siberia to the South Atlantic, his father, back home, is dying. But Atkins’s eye for the personal – Zulu chieftains with collapsing hairstyles, assassins with anxiety, a migrant family’s private grief – is matched by his acute awareness that this both is and isn’t all there is. The point at which personal and political become mutually inescapable: that, Atkins says, is where exile is.

Each of his subjects felt that tension keenly; each suffered a painful collision between their desires and the insensate demands of state and law: the catch and pull of history on the make. Michel saw the streets of Paris run red with blood when the Commune was suppressed in the semaine sanglante, the “bloody week”. Dinuzulu witnessed the end of his kingdom: Zululand was politically and spiritually dismembered by the British empire. Shternberg, a socialist Jew in tsarist Russia, endured brutal political repression alongside the lifelong threat of antisemitic violence.

It got worse. Michel was sent to New Caledonia, a French colony ill-at-ease with itself and with a brutally oppressed native population. Dinuzulu was stranded on Saint Helena – the same bleak South Atlantic islet Napoleon died on. Shternberg was immured on the “last refuge of the unshot”, Sakhalin island, in Siberia’s frozen east. All three could well have died. That was expected. Exile the noun is predicate on exile the verb. It’s always something done; something done to you. The powers that banished Michel, Shternberg and Dinuzulu had several names – Britain, France, Russia – of which only one really matters: empire.

Empire took Michel, Dinuzulu and Shternberg from their homes. Atkins identifies a subtler, more radical dislocation at work, too: empire took home from them. A people uprooted are a people undone; disquieted, doubtful, easy to control. The movement of exile – the movement of empire – carries us away from ourselves. Exile’s strongest moments are worked out in the shadow of this insight: a present-day fete on Saint Helena, lit by the half-life glow of the sun that never set; the crude commercialism and dying machines of post-Soviet Sakhalin; New Caledonia, still a colony, still ill-at-ease. The exiles outlasted their exile. But empire outlasted both.

Atkins’s subjects defied expectations; defied, in a sense, exile itself. Shternberg invents modern anthropology; Dinuzulu reinvents kingship. Michel goes further, dreaming of a time when exile, a tool of oppression, could become the sign and seedbed of liberation. She imagined building a house of exiles, a universal asylum for the dispossessed and the refugee. It would be built in London, where, she said, “my banished friends are always welcome”. We’ve come a long way; we’re still a long way from home.

• Exiles: Three Island Journeys by William Atkins is published by Faber (£20). To support the Guardian and Observer order your copy at guardianbookshop.com. Delivery charges may apply