Over 10 days, we visited just about every farm and homestead in the two principal islands. We were greeted everywhere - and we could see the slogans and the union flag from the air before we landed - with the same messages: "Chalfont Go Home" and sometimes "We Want To Stay British". The islanders were adamant. They wanted nothing to do with Argentina, and Chalfont left them with a promise that nothing would happen without their agreement. Fourteen years later, in 1982, Britain and Argentina were at war over the islands, and nearly a thousand people lost their lives. Today we are invited to recall the 25th anniversary of that event, and the Argentinian government has reminded us of its claim, pulling out of the 1995 agreement about joint oil exploration that had been fondly embraced by the Foreign Office as an alternative to discussing anything as conflictive as sovereignty.

People sometimes ask me why Argentinians make such an endless fuss about the islands they call Las Malvinas. The answer is simple. The Falklands belong to Argentina. They just happen to have been seized, occupied, populated and defended by Britain. Because Argentina's claim is perfectly valid, its dispute with Britain will never go away, and because much of Latin America is now falling into the hands of the nationalist left, the government in Buenos Aires will enjoy growing rhetorical support in the continent (and indeed elsewhere, from the current government in Iraq, for example), to the increasing discomfiture of Britain. All governments in Argentina, of whatever stripe, will continue to claim the Malvinas, just as governments in Belgrade will always lay claim to Kosovo.

The Falklands were seized for Britain in January 1833 during an era of dramatic colonial expansion. Captain John Onslow of HMS Clio had instructions "to exercise the rights of sovereignty" over the islands, and he ordered the Argentinian commander to haul down his flag and withdraw his forces. Settlers from Argentina were replaced by those from Britain and elsewhere, notably Gibraltar. Britain and Argentina have disagreed ever since about the rights and wrongs of British occupation, and for much of the time the British authorities have been aware of the relative weakness of their case.

An item in the Public Record Office refers to a Foreign Office document of 1940 entitled "Offer made by His Majesty's government to reunify the Falkland Islands with Argentina and to agree to a lease-back". Though its title survives, the document itself has been embargoed until 2015, although it may well exist in another archive. It was presumably an offer thrown out to the pro-German government of Argentina at the time, to keep them onside at a difficult moment in the war, though perhaps it was a draft or a jeu d'esprit dreamt up in the office.

The record suggests that successive UK governments have considered the British claim to the islands to be weak, and some have favoured negotiations. Recently released documents recall that James Callaghan, when foreign secretary in the 1970s, noted that "we must yield some ground and ... be prepared to discuss a lease-back arrangement". The secretary of the cabinet pointed out that "there are many ways in which Argentina could act against us, including invasion of the islands ... and we are not in a position to reinforce and defend the islands as a long-term commitment. The alternative of standing firm and taking the consequences is accordingly not practicable."

Of course, some people argue that Britain's physical possession of the islands, and its declared intention to hold them against all comers, makes its claim superior to Argentina's. Some believe that the Argentine invasion of the islands in 1982, and their subsequent forced retreat, in some way invalidates their original claim. Britain, above all, owes some debt to the heirs to the settlers who were originally sent there, a debt recognised in the Foreign Office mantra that, in all dealings with Argentina about the islands' future, the wishes of the islanders will be "paramount". Yet no such debt was recognised in the case of the inhabitants of Diego Garcia, perhaps because Britain inherited them from the French rather than planting the settlers themselves.

Ironically, the Falkland islanders are the outcome of a 19th-century scheme of settlement not very different from the experience of Argentina in the same century, which brought in settlers from Italy, Germany, England and Wales, and planted them on land from which the native Indians had been cleared and exterminated. The record of the islanders looks rather cleaner by comparison. Yet the Argentinian claim is still a good one, and it will never go away. At some stage, sovereignty and lease-back will have to be on the agenda again, regardless of the wishes of the islanders. Ideally, the Falklands should be included in a wider post-colonial cleanup of ancient territories. This would rid Britain of responsibility for Northern Ireland (almost gone), Gibraltar (under discussion), and for Diego Garcia (de facto given to the Americans), and anywhere else that anyone can still remember.

This post-colonial policy should have been adopted many years ago (and perhaps Harold Wilson's government was groping towards this end in the 1960s when Denis Healey abandoned British commitments east of Suez, and when Chalfont was sent to Port Stanley), and it should at least have been considered when we abandoned Hong Kong in the 1990s. Yet the strength of Blair's imperial revivalism, forever echoed in the popular press, suggests that this prospect is as far away as it was in 1982.

· Richard Gott's latest book is Cuba: A New History (Yale University Press)

rwgott@aol.com