A report to be published tomorrow recommends that Prince Charles should not take over the role when the Queen dies, but that a political figurehead should be chosen instead.
The centre, run by Mark Leonard, the New Labour whiz-kid who advised the Government on "rebranding Britain" and has drawn up plans to modernise the monarchy, also advocates annual elections for a new president of the Commonwealth to represent the views of member states.
The report further recommends that the running of the Commonwealth should be moved out of London to emphasise that the organisation has broken with the past and is no longer just a throwback to colonialism. A new Commonwealth Forum, involving ambassadors from all 53 member states, should be set up and meet regularly to discuss issues of concern, it says. At present the only opportunity for debate is the formal heads of Government meeting every two years.
The proposals, if implemented, would be the biggest shake-up of the Commonwealth since it was set up in its present form 50 years ago. They are likely to be received warmly by the Foreign Secretary, Robin Cook, who is President of the Foreign Policy Centre, because Labour has already pledged to review Britain's relationship with its former colonies.
Mr Leonard believes reform is long overdue. "If the Government is serious about turning Britain into a country that's proud to be multicultural and modern, we need to turn the Commonwealth into something that is more than just a hangover from the Empire," he said.
The report sets out the parameters for a full inquiry into the role of the Commonwealth, to be conducted by the Foreign Policy Centre over the next six months. The results will be published shortly before the next Commonwealth Heads of Government meeting, in South Africa in November.
The link between the monarch and the Commonwealth will form a central part of the investigation. The report argues that this is central to the image of colonialism and should be severed. "If you have got the British head of state as head of the Commonwealth then that looks like a continuation of the Empire," Mr Leonard said.
Although the Foreign Policy Centre stresses that the Queen has done a good job as head of the organisation, the proposal is certain to fuel republican instincts in Commonwealth countries around the world. A referendum on the role of the monarch is pending in Australia.
The investigation follows growing concern at the Foreign Office that the Commonwealth is misunderstood and widely seen as irrelevant. In a recent survey, 43 per cent of people said they did not know what the point of the Commonwealth was - despite the fact that two-thirds of schoolchildren have a relative in one of the member countries. There is also resentment among some Commonwealth states that although the body represents 1.6 billion people - a quarter of the world's population - it is still run entirely from London.
The report recommends that the Commonwealth Secretariat should be based in another country, possibly moving round the world on a rotating basis. It says that there should be a working president, elected by other heads of state, in a system similar to that used to choose the president of the European Union. And it urges the Government to appoint a Commonwealth "enforcer", who would be responsible for ensuring that all countries abided by common values on democratic elections and human rights.