European Union commissioner Chris Patten and senior judge Lord Bingham are the joint favourites to take the prestigious role.

Comedian Sandy Toksvig and Lord Neill, the former chairman of the committee on standards in public life, are the other contenders.

An estimated 20,000 of the 100,000 graduates eligible to vote did so.

The winner replaces Lord Jenkins of Hillhead, the former home secretary and well-known author, who died in January.

Tuition fees

The last such election took place in 1987, when his predecessor, Lord Stockton, the former Prime Minister Harold MacMillan, died.

On that occasion only 8,000 graduates took part, but the franchise has since been widened.

However, undergraduates were still not able to take part in this weekend's vote.

Much of the debate among the candidates has focused on whether the government should be allowed to introduce annual university tuition fees of up to �3,000.

Ms Toksvig, thought to be the favourite among undergraduates, was the only one to come out strongly against the proposal.

The voting, on a single transferable system, whereby second, third and fourth choices can be made, took place in the Divinity School in the university's famous Bodleian Library.