A free market in tuition fees in which universities will be free to charge more than £10,000 a year for courses is expected to be recommended by the government's official adviser on higher education next week.

Unveiling the most important report on higher education in decades, Lord Browne will say that universities should be allowed to keep all the income from tuition fees up to an annual level of £10,000. The current cap is £3,290. The Observer has learned that he will also recommend they be allowed to cross that threshold if they pay a rising proportion of the additional income into a central fund. The money could be used to support students from poorer families.

If they are accepted, the radical proposals by Browne, the former chief executive of BP, would amount to the most far-reaching shake-up of higher education in decades and could result in middle-class students leaving university with debts in excess of £80,000. It will be up to ministers how they respond to the plans.

Vince Cable, the secretary of state for business, innovation and skills, the department that includes universities, and David Willetts, the higher education minister, are said to be convinced of the need to increase fees, but only to the level of £7,000, and alongside "progressive" measures to help the poorest. The shock of Browne's recommendation, if he sticks to it, could make such plans appear moderate.

The issue of fees is toxic for the Liberal Democrats, with many of the party's MPs having signed a pledge to oppose any increase in fees. Senior figures such as former leader Sir Menzies Campbell have promised to rebel in any vote that would increase the levels that universities can charge. Campbell, who is chancellor of St Andrew's University, said yesterday: "My root objection is to students being saddled with mountains of debt by the time they leave university."

Aaron Porter, president of the National Union of Students, said: "If this is true, then Browne's attempt to deliver a free market in higher education is a proof that he is seeking to price out the poorer students. The average debt already is in excess of £25,000." Students would hold the Lib Dems to account, he added, in relation to the coming decision on tuition fees.

"The Lib Dems pledged to vote against higher fees, their party policy is a graduate tax, the coalition agreement states that student debt is of concern. It is completely inconceivable that the Liberal Democrats could vote for higher fees without completely losing the trust of students and their families," he said.

There was also opposition from unions representing university lecturers. Sally Hunt, general secretary of the University and College Union, claimed Browne had failed to take into account public opinion. His proposals would, she added, "simply be a way to squeeze more money out of students and their families". They would also sap the ambition of many students.

Others warned that they would drive apart universities and create a two-tier system like the one that existed before polytechnics were abolished in 1992. Professor Les Ebdon, chair of the university thinktank million+, many of whose members are former polytechnics, said: "It is a pretty big shove in that direction."

He claimed that many universities, particularly those with a higher proportion of students from working-class families, would feel unable to charge the full amount, resulting in a competitive market in fees.

Recent research shows that many of the prestigious universities that make up the Russell Group already take a far smaller proportion of working-class students than others.

Ebdon said the result of a student fee level of £7,000 would be that only the most socially elite universities could charge the full amount. "It creates a two-tier university system, one set of universities for the rich, one set of universities for the poor – one set of university experiences for the rich and one set of university experiences for the poor," he said. Ebdon argued that politicians "don't get it".

"There are two million students in this country and about 400,000 of them are taught in Russell Group universities. The vast majority of students are outside that."

• This article was amended on Saturday 16 October 2010. The original article said 40,000 students are at Russell Group universities. This has been corrected.