Royal car attacked in protest after MPs' fee vote
In angry scenes, protesters battled with police in Parliament Square. Hundreds were later contained on Westminster Bridge by officers.
Police say 12 officers and 43 protesters have been injured, while 22 arrests were made.
Prime Minister David Cameron said it was "shocking and regrettable" that protesters had attacked the prince's car.
Clarence House said the royal couple were safe and attending the Royal Variety performance as scheduled.
Metropolitan Police Commissioner Sir Paul Stephenson said there would be a "very serious and very detailed investigation" into the disturbances, in which 10 police officers have been injured.
The vote will mean fees will almost treble to £9,000 a year. The government's majority was cut by three-quarters to 21 in a backbench rebellion. Three ministerial aides resigned.
Only 28 Lib Dem MPs - less than half - voted for the government's plans for tuition fees. Six Conservative MPs voted against.
There were angry clashes as protesters - some throwing missiles - fought to break through police lines.
Riot police had to force back protesters who were smashing windows of the Treasury and the Supreme Court.
Earlier, protesters had largely taken over Parliament Square and pressed against lines of police in front of the Houses of Parliament.
Mounted police were used to control crowds, at one point charging a group of protesters, as thousands of demonstrators protested outside the Houses of Parliament.
Other reported actions taken by the protesters include:
- Setting the Christmas tree in Trafalgar Square alight
- Smashing windows at shops in Oxford Street
- Vandalising statues in Parliament Square, including that of Winston Churchill
- A sit-in by about 150 students at the National Gallery
Students from around the UK gathered in London for a day of protests and a rally - with police expecting about 20,000 demonstrators.
The coalition government faced its first major backbench rebellion in the vote.
The BBC's Ben Brown, outside Parliament, said protesters shouted "shame on you" as news of the result filtered out to the crowd.