Lord Sutherland said the money should go partly towards providing scholarships for disadvantaged students.

The former principal and vice-chancellor of Edinburgh University said a "postcode lottery" still exists in some places when it comes to entering higher education.

His call came as university leaders from across the UK gathered in the Scottish capital for their annual conference.

Lord Sutherland, who is also a former vice chancellor of the University of London, said: "South of the border they have fees. I believe they will increase the range of fees paid and Scottish universities will be less competitive as a result. That's just fact.

"One of the things universities do with their money is provide help and support for students who need the cash. Now I don't think there's going to be, in squeezed budgets, room to expand that in the way we should.

"If the fees are paid by those who can afford it - and some can because they've been paying very expensive school fees at private schools - then there's more room for universities to provide money for scholarships."

Up-front tuition fees were scrapped in Scotland by the first Scottish Executive.

Lord Sutherland said that university participation rates in Scotland have increased "dramatically", but he said more people from less well-off backgrounds should be going on to higher education.

"I think what you have to look at is the fact that in certain parts there's effectively a postcode lottery," he said.

"That's not on talent. Talent is spread across the whole community. It is on school results, so there's a gap there to be bridged."

Lord Sutherland said his plan was about heightening the aspirations of all students, and suggested more work also needed to be done at school level.

He said: "I think what's also needed is more help for schools in areas of some difficulty - that's where I think the Government has to be a partner.

"One of the key things is giving aspiration to students. One of the others is making sure that they get enough to overcome perhaps difficulties that other pupils don't have.

"That means, I think, more teachers in those classrooms."

The educationalist acknowledged that his proposals would not be universally popular.

He said: "It won't be welcomed by some and turkeys don't vote for Christmas, so I can understand that.

"But we have to decide how many people we want to go to university in Scotland."

He added: "You have to decide, of those, have you got a spread of where the talent really is?"

The Conservatives said Lord Sutherland was right to highlight concerns about the funding of higher education in Scotland and they called for review of higher education.

Murdo Fraser MSP, the party's education spokesman, said: "There are widespread concerns across the sector about what could be a growing funding gap between Scottish institutions and those in England.

"Scottish universities simply cannot afford to lose top quality academics, and cannot see investment in facilities fall behind those of our counterparts in England.

"No political party in Scotland supports the introduction of top-up tuition fees here. However, if we are not to have top-up fees, then some other source of funding has to be found, and it is probably unrealistic to expect all the additional cash to come from the taxpayer.

"We want an independently-chaired review of higher education in Scotland to address a wide range of issues, and specifically look at the funding challenge."

The University of Strathclyde Students' Association said they "strongly oppose" Lord Sutherland's position.

Association president Philip Whyte said: "Traditional students are still in the majority and differing demographics still face barriers to entry.

"In a city like Glasgow, widening access is of the utmost importance, with educational attainment opportunities based on ability not ability to pay, a must.

"The University of Strathclyde has a civic responsibility to ensure all those who wish to study are able to study free from the threat of top up fees."