Labour leader Ed Miliband has reached out to Liberal Democrat MPs who might rebel over plans to raise tuition fees.
Mr Miliband promised to work with any MPs in the House of Commons who supported a more "progressive" student funding system.
The Liberal Democrat Business Secretary Vince Cable has admitted that there will not be a graduate tax.
Lord Browne's review of tuition fees is expected to recommend a sharp increase - to £7,000 per year or higher.
Speaking on BBC1's Politics Show, Mr Miliband warned against creating a free market in tuition fees, which he said raised "the prospect of £5,000, £7,000 or £10,000 in fees".
"I'll work with anybody in the House of Commons who wants a progressive system of student finance," said Mr Miliband.
Labour's education spokesman, Andy Burnham, also attacked the idea of a market in different fee prices between universities.
"I worry greatly that we might be about to build a university system that is out of reach for ordinary families," he told the BBC's Andrew Marr programme.
"I do not want to see a pure market in university education where the best universities can practically charge what they like."
If the coalition government approves higher fees it will cause deep difficulties for Liberal Democrat MPs, who signed personal pledges that they would vote against any increase.
The National Union of Students has already warned Lib Dem MPs against such a "complete betrayal" of their promise.
Mr Miliband, whose own party introduced tuition fees, indicated that he was ready for cross-party co-operation in opposing higher charges.
Former Lib Dem leaders, Menzies Campbell and Charles Kennedy have already voiced concerns about the party ditching its election promise to oppose higher tuition fees.
Martin Shapland, chairman of Liberal Youth, says the Lib Dem leadership would be wrong to support higher fees - and called on members to mobilise against this.
Lord Browne's report on university funding in England is due to be published on Tuesday - but Business Secretary Vince Cable pre-empted this on Saturday evening, by publishing a letter announcing that there would not be a graduate tax.
This has been seen as paving the way for the announcement of an increase from the current £3,290 a year - either to a higher level of tuition fees such as £7,000 per year or to withdraw the upper limit altogether.
But Mr Cable highlighted his continuing support for a "progressive" element to the fees system.
This is expected to mean charging a higher rate of interest on student loan repayments for graduates who enter higher-paid jobs.
Less well paid graduates would be expected to pay at a lower interest rate.
The Conservatives appear to have accepted this income-related repayment side of the fees package.
Transport Secretary Philip Hammond, speaking on the Andrew Marr Show, described a system of variable interest rates for student loan repayments, once people have graduated and entered work.
This would mean that "those with the lowest incomes have their interest rate effectively subsidised, while those on the highest incomes provide something additional to provide that subsidy".
As well as raising fees and introducing a variable interest rate for repayment, Lord Browne's review is expected to announce a student charter, to ensure students get value for money.
University leaders have also warned that budget cuts expected in the forthcoming spending review could mean that increased student fees will be used to replace withdrawn public funding, leaving universities without any real increase.