Emboldened by the numbers who took to the streets of London to campaign against the proposal to charge up to £9,000 a year in fees, students are planning a wave of direct-action protests across the country.

Protesters occupied a building at the University of Manchester today, demanding access to accounts to see how government spending cuts may affect students and staff.

Grassroots groups were drawing up plans for a national day of action in two weeks' time. Michael Chessum, the co-founder of the National Campaign Against the Cuts, predicted there would be widespread disruption as students staged sit-ins, occupations or walkouts at universities and colleges on 24 November.

"We went off script: the script that said a few thousand people would turn up, complain a bit, and go home; and the cuts would go through pretty much as planned," said Chessum, 21, a sabbatical officer at University College London. "That has changed. Now students really feel they can stop this."

A statement published by student leaders praised the storming of the building housing Conservative party headquarters by a fringe group of protesters on Wednesday. "We reject any attempt to characterise the Millbank protest as small, 'extremist' or unrepresentative of our movement. We celebrate the fact that thousands of students were willing to send a message to the Tories that we will fight to win. Occupations are a long established tradition in the student movement that should be defended."

The statement was signed by Clare Solomon, president of the University of London Union, Cameron Tait, president of Sussex University's student union and Lee Hall, author of Billy Elliot, among others. It puts local student representatives at odds with the NUS national leadership, which condemned Wednesday's violence.

The Millbank protesters were also praised by the president of the lecturers' union at Goldsmiths, London, who said their actions had brought attention to the cause. John Wadsworth said: "Yesterday was a really good natured but equally angry demonstration against the damage that the coalition is doing to higher education.

"The real violence in this situation relates not to a smashed window but to the destructive impact of the cuts and privatisation that will follow if tuition fees are increased and if massive reductions in HE funding are implemented."

The NUS plans to campaign locally against Lib Dem MPs, reminding them of their pre-election pledge to vote against a rise in tuition fees that will apply in English universities. NUS president Aaron Porter said: "Its an issue of principle. Clegg talked about no more broken promises – they made a promise, and we will hold them to it." The union plans to raise petitions in constituencies with high numbers of student voters, warning MPs that they face losing their seat if they break their word on fees.

A number of Lib Dem MPs plan to vote against the proposal, due to be presented to parliament before Christmas. The 20 Lib Dem ministers, including Nick Clegg, the deputy prime minister, and the business secretary, Vince Cable, are expected to vote in favour. The resolution must be passed by both houses but cannot be amended. Clegg today admitted he should not have signed the NUS pledge on fees, blaming the state of public finances for the party's U-turn.

"I should have been more careful perhaps in signing that pledge," he said. "At the time I really thought we could do it. I just didn't know, of course, before we came into government, quite what the state of the finances were."

Writing in the Guardian today, Lib Dem MP Tim Farron describes fees as "the poll tax of our generation". He writes: "It is not for me to tell colleagues how to vote, but I believe that we need to move away from burdening young people with debt, towards a fairer system. Education should be available to all – not just those who can stomach the debt."

Lib Dem MP Lorely Burt said the party was "stuck between a rock and a hard place". She added: "This is not our policy. We are not comfortable with it. In the coalition agreement we didn't manage to get our own policy but we have modified the Browne report [on higher education funding] to inject a considerable amount of fairness and progressiveness into the programme."

Lib Dem opponents of a rise have not coalesced around an alternative policy. Martin Horwood, who plans either to abstain or vote against, said: "The long-term alternative is really to pay for student finance through income tax and probably an inevitable reduction in student numbers, neither popular options with our Conservative partners. So short term, I fear the alternative would be cuts in other areas like science or FE, which is why I'm hesitating to vote against."

Student protests today included a three-hour sit-in by 60 students at Manchester, demanding access to the university's accounts. "This is just what a few students who had the energy left after the London demo managed to achieve," said Jeremy Buck, 22.

In Cambridge, students protested at the university's annual science, engineering and technology careers fair against "the marketisation of education".