Come with me towards the Equator, first 5,000 miles east, then 5,000 miles west of Africa. We shall visit tiny specks of land: islands notionally our own. This month, the inhabitants of one have voted to re-establish their island council. And last week the former inhabitants of the other lost their battle for a right to return.

First, though, lest you be tempted to think that cynicism, duplicity and spin are to the special discredit of today's politics, read this:

“The object of the exercise is to get some rocks which will remain ours; there will be no indigenous population except seagulls, who have not yet got a committee. Unfortunately, along with the seagulls go some few Tarzans and Man Fridays, that are hopefully being wished on Mauritius.”

This is extracted from an internal Whitehall note circulated at the time when the Foreign and Commonwealth Office was stealing from the inhabitants of the Indian Ocean Chagos Islands their birthright, shipping them to newly independent Mauritius, washing Britain's hands of responsibility and handing over the largest island, Diego Garcia, to the Americans, to whom successive British governments were sucking up. In 1966 we gave America what is effectively a 50-year lease. We got nothing in return except, it is rumoured, a notional discount on some Polaris missiles. There were some two thousand of those “few Tarzans and Man Fridays” and they had been there for two generations before being conveniently reclassified as temporary workers. We lied and lied and lied again about this.

Since then the US writ has run on Diego Garcia; its airbase there has become key to US defences, vital for Iraq and Afghanistan. The poor Chagossians and their descendants (also called Ilois) have stewed in slums in Mauritius with derisory compensation; or washed up in the Seychelles or Crawley, by Gatwick.

This is no place to reprise their story - I told it in The Times many years ago when Tam Dalyell, MP, was fighting for the Ilois - so suffice it to say that they have won court battle after court battle for the right to return (the Government's case having been found a “repugnant” attempt to “exile a whole population”), until finally losing in the Court of Appeal last week. Everyone knows the underlying reason why they lost: “Too bad,” it is thought, “but we cannot put Humpty Dumpty together again.” The saga is a stinking disgrace, a slur on Britain's good name, a slur on the FCO, a slur on the Ministry of Defence and a slur on ministers past and present.

The Chagossians may appeal to the European Court of Human Rights, but a Whitehall that has successfully denied them justice for a quarter of a century will find the ingenuity to continue blocking their return. Everybody knows why. It's the Americans. They want this archipelago to themselves. The US military call Diego Garcia alternatively “Camp Justice” and “the Footprint of Freedom”. It is used for “extraordinary rendition” flights. David Miliband, the Foreign Secretary, knows that, too - or, rather, has understood the benefits of not examining Washington's story too closely.

Across the other side of Africa lies Ascension Island. The impression I had when I visited was of a volcano rising out of the middle of the Atlantic, and on its skirts another big American airbase - Wideawake airfield. Ascension, too, is a British possession, ruled in theory from distant St Helena, and slightly less theoretically by a resident British administrator, and more in reality than theory by the US military.

During the Second World War, Washington built an airstrip; in 1957 a US presence was re-established, and its occupation of the base has been renewable annually by consent ever since. Britain is paid nothing: indeed we have to pay the Americans $1,000 every time one of our civil aircraft lands there.

During the Falklands war the Defence Secretary, John Nott, was astonished when the Americans at first refused Britain's request to refuel Vulcan bombers at Ascension: an “intolerable and disgraceful episode”, he wrote in his memoirs Here Today, Gone Tomorrow, that he thought could only have come from General Alexander Haig. Washington did back down - but that a US Secretary of State could have even tried to deny us use of our own island to defend our own possessions tells us something we ought to hear about our ally.

On Ascension, the civilians working there have never been given settlement rights. Nine years ago the British Government began to remedy this and gave the islanders their own elected council. Then Britain changed its mind about settlement rights, citing the “contingent liabilities”, though no breakdown of the costs was divulged. The elected council resigned in protest. This month a new election was held. Nobody really knows how far down the road to rights for locals the British Government is prepared to go. My guess is that the problem is the Americans.

So what next in Diego Garcia and Ascension Island? Now - as some faltering democracy is re-established for civilian residents of Ascension and as the Chagossians finally lose their fight to return - is a good time to take stock.

In both possessions we British get the continuing colonial stigma, while America gets the practical use. In Diego Garcia the Americans are well on the way to de facto possession. We cannot stop them using the place for torture flights; it is inconceivable that we would thwart them there in any military purpose. To us, this possession is a source only of shame. It serves no national interest beyond its use to an ally.

We should cede it to America. With eight years of the present agreement left to run, London should talk to Washington about selling the possession for an eye-watering sum; compensate its former inhabitants and their descendants generously; and pocket the rest. Diego Garcia is vital to US military strategy; $15billion should be our opening bid.

Ascension Island is different. Important to St Helena as a staging post and relatively close to Tristan da Cunha, the airfield is vital for flights to the Falklands. Possession gives rights for offshore oil. Nor have we ever allowed the Americans a long lease there. Our position has not eroded so completely as on Diego Garcia. We should renegotiate, offering a longer lease, defining more clearly what is ours, exacting a proper rent and requiring US consent for a decent status for civilians.

Ministers will say: “Why now?” But the why-now moment is often the right moment: a time when all sides have some slack to play with. At present, nobody is suggesting using Diego Garcia for bombing raids on Iran or setting up a mini- Guantanamo there; the airfield at Ascension isn't at the centre of any new tension with Argentina over oil; and the workers aren't on strike over their Cinderella status.

Nobody's very interested in Ascension Island or Diego Garcia. Not now. Not yet. The moment is propitious. Seize it.

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