The Prince of Wales and the Duchess of Cornwall were attacked by protesters last night as tuition fees demonstrations turned violent.

Prince Charles and Camilla were unharmed after their car was hit by paint as they made their way to the Royal Variety Performance in central London.

Police and protesters were taken to hospital following a series of running battles in the Westminster area after MPs voted to hike tuition fees to up to £9,000.

Protesters attacked a number of Government buildings near the House of Commons, smashing windows at the Treasury and the Supreme Court and vandalising statues in Parliament Square, including that of Winston Churchill.

The chaos spilled out on to Oxford Street as a number of demonstrators continued their protest.

Police condemned the behaviour, with Superintendent Julia Pendry describing the demonstrators’ actions as “outrageous”

She added: “This is not peaceful protests at all ­– this is acts of wanton vandalism, wanton violence and a complete disrespect for central London... We have now got a number of protesters rampaging their way through London, committing acts of violence, acts of terror, not only to Christmas shoppers and to tourists but to innocent people in London going about their business tonight.”

Some 38 protesters and 10 officers were injured. Six officers required hospital treatment and four suffered minor injuries. Some 20 people were arrested: nine for violent disorder, two for arson, two for assault on police, two for criminal damage, one for being drunk and disorderly and four for burglary

Earlier yesterday the government coalition suffered three resignations and saw its majority slashed as the Liberal Democrats split three ways over moves to hike tuition fees to up to £9,000.

As violence raged outside the Commons, 21 of the party’s MPs defied desperate pleas from leader Nick Clegg and voted against the controversial rise with eight not voting. The Government won the vote to raise fees with a majority of just 21.

It was the first real test for the Government which has a notional majority of 84. Some 323 MPs were in favour and 302 against.

The vote came after a tense five-hour debate in the Commons, which saw a number of Lib Dem MPs and a handful of Tories voice opposition to the plans.

Violence flared as thousands of protesters descended on Westminster to demonstrate against the hike.

Two Liberal Democrat MPs resigned as ministerial aides ahead of the vote. And Tory MP Lee Scott, an aide to Transport Secretary Philip Hammond, also quit after abstaining in the vote.

Mike Crockart, parliamentary private secretary to Scottish Secretary Michael Moore, was the coalition Government’s first casualty, quitting in order to vote against the proposals. Jenny Willow has also resigned.

Business Secretary Vince Cable said earlier that he was “proud” of the Government’s package, which will come into force in English universities from 2012. He insisted the package was “progressive” and would “maintain high quality universities in the long-term”.

As MPs debated the issue, as many as 30,000 students, lecturers, parents and union members took part in a last-ditch demonstration against the hike.

There were violent skirmishes between police and protesters in Parliament Square, as officers were pelted with flares, sticks, snooker balls and paint balls.

Wooden benches in Parliament Square were set on fire, and two demonstrators were seen standing on top of the bonfire, watched by cheering protesters.

As scuffles continued to break out, police began using the controversial tactic of “kettling” protesters in Parliament Square.

Some 19 people have been treated by paramedics, six of whom were taken to hospital, London Ambulance said.

A second Commons vote, again won by a reduced majority of 21, confirmed that the new basic fee cap will be £6,000.

It means England’s universities will be able to charge up to £6,000 per year in fees from 2012, and as much as £9,000 in “exceptional circumstances”. This is treble the current £3,290 cap for 2010/11.

The issue has been highly contentious for the Lib Dems who have found themselves under fire over the plans. They publicly pledged before the election to scrap the fees and vote against any increase.