Charles and Camilla were unharmed after their car was struck and daubed in paint as they made their way to the Royal Variety Performance in central London.
When the royal couple arrived at the theatre, they appeared relaxed, and smiled and joked with Kylie Minogue, Take That and N-Dubz, some of the acts who performed for them tonight.
Outside, their Rolls-Royce limousine was left with a badly-cracked passenger-side rear window and was spattered with paint thrown in the Regent Street attack.
Scotland Yard condemned the "outrageous and increasing levels of violence" tonight.
A spokesman said: "This has nothing to do with peaceful protest. Students are involved in wanton vandalism, including smashing windows in Oxford and Regent Streets.
"Innocent Christmas shoppers are being caught up in the violence and disruption."
Those being held in Parliament Square, especially the young and vulnerable, were being allowed to leave in small numbers via Whitehall, police said, and those in the containment were able to get water and use toilet facilities in nearby Great George Street.
Police and protesters were taken to hospital following a series 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.
"Not only have we had attacks on Parliament, the attacks on our officers, we've now had the Supreme Court that has come under the attack of vandalism and the Prince of Wales and the Duchess of Cornwall have also come under attack in Argyll Street.
"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.
"It is appalling, disrespectful behaviour to everybody else in London."
Prime Minister David Cameron's spokeswoman also said he condemned the "unacceptable" violence.
Some 38 protesters and 10 officers have been injured. Six officers required hospital treatment and four suffered minor injuries.
So far 20 people have been 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.
A spokeswoman for London Ambulance Service said that by 8.30pm they had treated 37 people, of whom 31 had been taken to hospital.
She could not confirm how many of the injured were police and how many were protesters.
Metropolitan Police Commissioner Sir Paul Stephenson said: "It's been a very long day, it's been a very stretching day for the Metropolitan Police Service and it has been a very disappointing day for London, in my opinion.
"We did everything we could to facilitate peaceful protest and, in reality, whilst I'm sure the vast majority came here to want to protest peacefully, a significant number of people behaved very badly today."
He added: "We want to see people peacefully protesting on the streets of London if that's what they wish to do, but the behaviour today is wholly unacceptable and we will now mount a very serious and very detailed investigation to try and identify the perpetrators of the violence today."
Sir Paul rejected claims that the police had exacerbated problems by containing the protesters.
He said: "I think that is, frankly, utter nonsense. I think anybody who has been watching the pictures of the violence today will just want to condemn it.
"Any right-minded individual, including peaceful protesters who want to make a point, will condemn what has happened today and, frankly, that is just an excuse that people are hiding behind and it is not acceptable."
A spokeswoman for London Mayor Boris Johnson said: "The Mayor is appalled by the scenes of violence this evening.
"There is no excuse, whatever one's view of the vote in Parliament, for the destruction and aggression seen today. It is an insult to democracy."
By 9.10pm the number of arrests had risen to 22 - one for being drunk and disorderly, three for criminal damage, two for arson, nine for violent disorder, three for assault on police and four for burglary.
Nick Littler, 20, a student from Royal Holloway, said: "After the vote, everyone was miserable and we were all just drifting away. The police were letting one person out every 10 minutes."
Protesters were swept out of the square by police over Westminster Bridge.
One woman who was caught up in the protest as it descended on Argyll Street, in the centre of the West End, spoke of her fear over the incident.
Jessica Vieira, a 25-year-old fashion company employee, said: "They closed off the (Oxford) Circus station and all the police were pulling everybody back.
"The guys were lighting bins and throwing them around, the police were getting a little bit hectic.
"It was pretty scary. I came out on my own to meet someone and couldn't get back to the station.
"I was locked in the pub - it's a hard life!"
Protesters were kept on Westminster Bridge between lines of police four rows deep.
The officers swept Parliament Square, forcing hundreds on to the bridge.
Matthew Fellows, 21, a student at Royal Holloway, said: "I understand the need to control people but the way they have done it, they were asking for trouble to happen. It's as if they have never dealt with a situation like this before."
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