It has welcomed democrats and dictators, Botswanans and Barbadians, but on the weekend, the Commonwealth received its most unexpected guest of all, a French president.

In a curtain-raiser for the Copenhagen climate talks and a reversal of centuries of imperial rivalry Nicolas Sarkozy joined the UN Secretary-General and Danish prime minister in making the case for an agreement on carbon emissions. There had even been excitable reports swiftly denied that Barack Obama would jet in, hoping to woo the 53 members before the real bargaining begins.

Such diplomatic hurdy-gurdy reflects the fact that the Commonwealth has a membership unlike any other world body. As Tony Blair said in 1995, it "includes five of the world’s 10 fastest-growing economies … It is the only organisation, outside the UN itself, to transcend regional organisations and bring together north and south. The issues that dominate post-Cold War relations are at its heart; refugees, drug trafficking, international crime, terrorism, Aids, debt and trade."

Since then, the rise of India has only increased the organisation’s potential significance especially for a Britain struggling to keep its place in the world.

In the old days, talk of the Commonwealth as "modern" or "vital" would have been bizarre. It was sometimes joked that ‘CHOGM’ the acronym for the biennial Commonwealth Heads of Government Meetings stood for "cheap holidays on government money", given that the centrepiece was a weekend retreat at which leaders chatted and negotiated as equals, free from the supervision of interpreters or civil servants.

Which other summit would see Margaret Thatcher waltzing arm in arm with the president of Zambia, the Queen offering cocktails to journalists on the Royal Yacht, or Blair lining up tennis matches against anyone his officials thought he could beat?

It wasn’t exactly that CHOGM was just a jolly apart from the networking, there was serious business to attend to. In Trinidad on the weekend, leaders discussed the readmission of Zimbabwe, and the arrival of Rwanda.

There was also to be warm talk about historic links and shared democratic values. But underpinning it all was the perennial question: what is the Commonwealth actually for? A report published on Thursday by the Royal Commonwealth Society warned that it has "a worryingly low profile" among both public and policy-makers: less than a third of people in the Commonwealth could name anything the association did, and the majority of those could cite only the Commonwealth Games.

Certainly, from the British perspective, the organisation has usually played second fiddle. Yet the Commonwealth has potential. Amid the West’s obsession with China, it is easy to forget that India with its far more savoury political system is also on the path to becoming a great power, hailed last week by Obama as a nation whose relationship with the US would help define the 21st century.

"I’ve been predicting for years that India is going to be the leading player in the Commonwealth," says Derek Ingram, a journalist and leading Commonwealth observer, "and it’s now coming to pass. Prime Minister Manmohan Singh is putting it at the centre of Indian foreign policy."

Within the organisation itself there has been no struggle for power it is far too gentlemanly a body for that but India is nevertheless starting to flex its muscles: it provides the current secretary-general, will host the next Commonwealth Games, and is increasing its funding for a number of the group’s initiatives.

For Britain, a Commonwealth in which India took a lead would be more of a club of equals, a better reflection of the changing world. It would also, economically speaking, be a way to hitch a ride on the back of the Indian tiger.

Yet whatever happens, Britain’s diplomats can reflect, as they bask in the Trinidadian sun, that what many have written off as an imperial relic has turned out to be a consensual, informal and adaptable organisation and one that could, if policy-makers show some vision, be uniquely useful in a world whose problems are beyond the scope of individual countries, or even continents.