Police have dispersed the final student demonstrators in central London after a day of protests against higher tuition fees and university cuts.
Police said 17 people were injured, including two officers as protesters were contained on Whitehall.
There have also been occupations in at least 12 universities, including Oxford University's Bodleian Library.
School pupils walked out of lessons to join university and college students on local protest marches across the UK.
As darkness fell, fires were started, graffiti sprayed and windows broken in Whitehall by demonstrators who were being contained by police.
Hundreds of remaining protesters were gradually released by police throughout the evening.
Earlier a police van was attacked and barricades thrown as protesters tried to break through police lines.
There were 32 arrests - mainly for public order offences and criminal damage, according to the Metropolitan Police.
Among the 17 people injured, the two officers and 11 members of the public were treated in hospital for minor injuries. No-one was seriously injured.
Transport for London (TfL) also reported that protesters had thrown missiles at buses in central London, smashing windows and causing many routes to be diverted away from the Whitehall and Trafalgar Square area.
Broken windows were reported on two routes, although no injuries were sustained.
A spokeswoman for TfL said: "We're still trying to assess the full extent of the damage from today's demonstrations.
"We know that bus shelters and ticket machines along Whitehall have been severely damaged and we're checking to see what other damage has been caused. As the protest moved on during the day we had to put in place rolling diversions to keep buses away from it."
The prime minister's spokesman said: "People have a right to engage in lawful and peaceful protest, but there is no place for violence or intimidation."
Protesters in London had intended to demonstrate outside the Liberal Democrat headquarters - with students accusing the party's leaders of planning to break their signed pledge that they would vote against higher tuition fees.
Speaking on BBC Radio 2, Mr Clegg said: "I hate in politics, as in life, to make promises that you then find you can't keep. We made a promise we can't deliver - we didn't win the election outright and there are compromises in coalition."
Students staged occupations at universities including Royal Holloway College, Plymouth, Warwick, Birmingham, London South Bank, University College London, Leeds, Essex, Cardiff, Sheffield and UWE Bristol.
In the iconic Bodleian Library in Oxford, students planned to hold a "teach-in" as part of the occupation.
In Birmingham, students called on the university authorities to reject what they call a "socially regressive plan that will limit access to education".
Students staging an occupation at University College London said they were protesting against "savage cuts to higher education and government attempts to force society to pay for a crisis it didn't cause".
Universities Minister David Willetts said students had not seemed to have understood the proposals on fees - and that they would not have to pay the higher fees up-front.
"Young people will be provided with the funds they need to meet whatever charges universities levy," said Mr Willetts.
Marches, walkouts and protest events took place at universities and colleges across the country.
There were protest marches in Manchester, Liverpool, Brighton and Bristol.
School pupils walked out of lessons in Winchester, Cambridge, Leeds and London.
Students were protesting against plans to increase tuition fees in England to £9,000 per year and to withdraw public funding for university teaching budgets for many subjects.
A much larger student march in London two weeks ago ended in an attack on the Conservatives' headquarters building - with the disturbances leading to 68 arrests.
In the protest on Wednesday, marchers were stopped by police on Whitehall, before the demonstration had reached Parliament Square.
There were crowd surges and attempts to break through - but the police cordons contained the protest.
Among those within the crowd held by police was 19-year-old Sam Lathwood.
"The protest started peacefully - everyone around me wanted a positive outcome. But there are people here who are not in education, taking advantage," he said.
"It's a disgrace. Things like this give students a bad name."
Protest leaders have claimed that an "unprecedented wave of student revolt is unfolding" - and they say they are following in the spirit of student protests of 1968.
Many of the events and walkouts have been organised using social networking websites.
University occupations are running their own blogs and websites.
As well as the planned rise in tuition fees, students are also campaigning about wider budget cuts for higher education.
Further education students and sixth-formers are also protesting at plans to remove the education maintenance allowance, which gives low-income students up to £30 a week to help with the costs of staying in full-time education.
Lewis Coyne, one of the organisers of a protest march in Liverpool, said: "It is important to get the message across that we aren't happy about what they are doing to the education budget and the rise in fees."
The fees protest held two weeks ago in Westminster was attended by an estimated 50,000 students - and ended with a breakaway group forcing their way into the Millbank office complex.