Students are warning the poor will be priced out of university if proposals to lift the cap on university tuition fees are passed.
They took to the streets over recommendations which could bring a market in university fees in England.
In Sheffield, students marched to the office of local MP and Deputy Prime Minister Nick Clegg.
They called on him and other Lib Dems to honour pre-election pledges to vote against any fee increase.
The former Lib Dem leader Sir Menzies Campbell has promised to do so, as have a few other MPs.
The demonstrations follow publication of the long-awaited review into student fees and higher education, led by Lord Browne.
The main recommendation is for a lifting of the cap on what universities in England can charge undergraduates for their courses - currently pegged at just over £3,000 a year.
The president of the University of Sheffield Students' Union, Josh Forstenzer said: "If the Browne Report is adopted it would condemn graduates to crippling debts of more than £45,000 and do nothing to widen access to universities.
"University access would be less about academic ability and more about the ability to pay. People from less well off backgrounds would have to choose where to study based on cost, whilst the rich would be able to study at elite institutions across the country.
"The support available for students from less well-off backgrounds is utterly inadequate. The spin around support for poorer students is just that. Higher fees will deter students from all but the wealthiest families from applying to university."
Hundreds of students also took to the streets in Birmingham and Edinburgh.
Students in Scotland do not pay fees now but there are growing calls for graduates to make a contribution to higher education there.
Students and academics are planning a mass demonstration in London next month against higher fees and the looming cuts to higher education expected to be announced in the Spending Review next week.
Students met across England on Tuesday to voice their anger over the proposals from Lord Browne's review.
If brought in, the current £3,290 cap on tuition fees would be scrapped and replaced by a free market, in which universities would set their own charges for different courses.
As is the case now, students would not have to pay fees upfront, but would receive a loan to cover them.
Students at Oxford University say the proposed changes would price many people out of higher education.
Martha Mackenzie, student president of St John's College said: "Students at Oxford are shocked at the recommendations from the review.
"Letting leading universities charge unlimited fees will price students out of higher education and threatens to irreversibly damage access to Oxford."
Lord Browne says the proposal is for a progressive system which would lead to the bottom 20% of earners paying less than under the current system.
Now part of the coalition government, Lib Dem MPs will be weighing up whether they stick to their promises or abstain when the issue comes to the Commons for a vote - as their coalition deal with the Conservatives allows.
The party had pledged to phase out fees over six years and had strong support in many university towns.
Lib Dem Business Secretary Vince Cable has said the party's previous pledge is "no longer feasible" and deputy party leader Simon Hughes said MPs now had to reflect on the arguments and "make their own choice".
The BBC's political editor Nick Robinson said the Lib Dems would not commit to abstain on the issue because it was so important to their support in university towns and they hoped to get more concessions out of the government.
The former Lib Dem leader Sir Menzies Campbell has said he will vote against any rise in tuition fees.
He told the World at One programme on BBC Radio Four: "Not only did I sign a pledge, I was photographed doing it".
Sir Menzies, a former chancellor of St Andrews university in his North East Fife constituency, added: "My credibility would be shot to pieces if I did anything other than stick to the promise I made.
"As for others, they must make their own judgment depending on their own circumstances."
Aaron Porter, the president of the National Union of Students said: "As the protests around the country demonstrated yesterday students are appalled at the proposals in the Browne review and deeply concerned by Vince Cable's reaction to it.
"Cutting funding to universities and passing the debt on to students is unacceptable and unsustainable and students, their families, staff and others will come together in London to protest in November.
"We look forward to working with all Liberal Democrats over the coming days and weeks to ensure that they can keep their pledge to vote for students."
If accepted by the government, the changes would take effect in 2012 at the earliest.