Demonstrators scuffled with riot police and made a bonfire in front of the building, located a short distance from the Houses of Parliament.
It was the first violent protest against 81 billion pounds ($130 billion) of spending cuts ordered for the next four years by the Conservative-Liberal Democrat coalition to tackle a record budget deficit.
Until now Britain has so far seen only muted anti-austerity protests compared with those which have rocked other European countries such as France and Greece.
Police said at least eight people had been injured, including a number of officers. Some rooftop protesters hurled placards and other small missiles onto the police below them.
The violence broke out during an otherwise peaceful march by thousands of students and lecturers protesting against plans by the Conservative-Liberal Democrat coalition to triple the amount universities in England can charge students for tuition.
Carrying placards saying "Stop education cuts" and chanting "They say cut back, we say fight back", the marchers passed parliament, where politicians will in the coming weeks vote on proposals to lift maximum tuition fees to 9,000 pounds ($14,500) a year.
"My parents are both public sector workers. My dad will lose his pension next year and my mum will lose her job and this will just put them in bankruptcy," said Matthew Kell, 22, from Bristol University in southwest England.
Other students on the march said they were demonstrating on behalf of their younger siblings, who will be liable for the higher fees when they kick in from 2012.
"My sister is 15, I doubt she will go away to university because it is so expensive," said Catrina Miles, 21, from Sheffield University, northern England.
Trade unions have forecast there will be large-scale strikes against the deficit cuts, which are expected to lead to half a million public sector workers losing their jobs.
The National Union of Students (NUS), which helped organise the march, condemned the action of "troublemakers" who had hijacked the protest.
"We talked about the need to prevent anything like this and how important it was to act in a responsible way. Unfortunately a minority have undermined us," NUS President Aaron Porter told BBC television.
The coalition government plans to cut 2.9 billion pounds of state support a year for universities to help tackle a budget deficit which soared to near 11 percent of gross domestic product following the global financial crisis.
It says the higher student fees, financed by government-backed loans, will cover the shortfall and allow Britain's universities to continue competing against international rivals.
