The Metropolitan Police said two officers were injured in London, including one with a broken arm. Three protesters were arrested.
College and university students across the country held marches and sit-ins to oppose the decision to increase university fees to 9,000 pounds ($14,000) a year, a key plank in the government's deficit-cutting austerity measures.
In central London, the university students and younger pupils in school uniforms marched from Trafalgar Square toward the Houses of Parliament, chanting "no ifs, no buts, no education cuts."
Some climbed on top of bus shelters, while several attacked a parked police van, smashing the windows and scrawling graffiti.
"Education is not a rich kid's game," said Tash Holway, 19, a student. "If this keep up, the entire industry will change. It won't be about talent, but only about who can pay."
Lines of police guarded the headquarters near Parliament of junior government partner, the Liberal Democrats. The Lib Dems have drawn particular anger because the party campaigned on a promise to abolish tuition fees, then abandoned it once in power.
The party leader, Deputy Prime Minister Nick Clegg, said Tuesday "I massively regret finding myself in (the) situation" of not being able to keep this promise.
Asked how he felt about seeing students burn him in effigy, Clegg told BBC radio: "I'm developing a thick skin."
There was a heavy police presence, with hundreds of uniformed officers on duty. Students complained about confrontational tactics.
"At first the march was peaceful and then the police were called in and started kettling people and not letting anyone out," said Mara Payne, 25, of south London.
Kaya Wiley, 17, said government is breaking its promises.
"They're wasting our money and we're not going to get anywhere," she said. "I don't want work at (supermarket) Tesco. I want to be able to go to university. I don't think the violence is effective and I'm afraid the government might just brush it off."
There were demonstrations several thousand strong in university towns and cities across the country, including Bristol, Liverpool, Sheffield and Leeds.
In Cambridge, hundreds of students scaled the fence outside Senate House, the building used for graduation ceremonies, and marched into the grounds of the 700-year-old King's College shouting and waving placards. Two people were arrested for obstructing police.
An 18-year-old British student pleaded guilty Wednesday to throwing a fire extinguisher off the roof of the high-rise building during the protest in London two weeks ago. It narrowly missed police officers standing below.
Edward Woollard admitted one count of violent disorder. His lawyer said Woollard was "very sorry for his actions."
District Judge Nicholas Evans said Woollard would be sentenced later. He faces a maximum of five years in prison.
Jill Lawless contributed to this report.