The Prince and Duchess were “unharmed” and continued with their engagement at the London Palladium, a Clarence House spokesman said.
The attack occurred on Regent Street at the end of a day of protest that turned into a riot and left 10 police officers injured, six of them seriously.
Matthew Maclachlan, who witnessed the attack on the Prince’s car, said: “The police cars at the front of the convoy drove straight into crowds at the top of Regent Street. They got trapped in that mob and it meant that Charles and Camilla were on their own further down the road except for a Jaguar travelling behind them.
“Charles and Camilla’s car ran into such a concentration of people that it had to stop. It was stationary for a lot of the time, then would squeeze forward an inch. They had just one bodyguard in the car with them and a chauffeur.
“We couldn’t believe it. The car had really big windows so Charles was very much on display. People were trying to talk to him about tuition fees at first but when more people realised what was happening, the crowds swelled and people were throwing glass bottles and picking up litter bins and throwing them at the car. You could hear all this smashing.
“There was one protection officer in the Jaguar behind, dressed in a tuxedo, and he was opening the car doors and using them to bash people away. His car took a real pummelling.
“It must have been frightening for them but, throughout it all, Charles was really calm and smiling at everyone. Camilla was beaming too. He was holding his hands out towards them in a gesture that said, 'I’m innocent’.”
Mr Maclachlan, who was not involved in the protest, said he was astonished that the police had taken that route.
“I don’t know why they went that way. It was the same crowd that had been in Trafalgar Square earlier, setting fire to the Christmas tree. There were so many protesters and they drove right into the middle of them.”
Although the rear window on the Prince’s side of the car was shattered, it did not break. The burgundy Rolls-Royce Phantom VI, used by the Queen on several previous occasions, is fitted with toughened glass as a security measure.
The incident raises serious questions about the policing of the protests, which came as MPs voted in favour of the policy of increasing the fees cap to £9,000.
They did so as the smell of fires burning outside in Parliament Square filled the chamber. The Government’s majority fell from 84 to 21 and the Coalition suffered three resignations.
In the run-up to the vote, up to 30,000 students had laid siege to the square and, in chaotic running battles with a mob, one mounted officer was knocked from his horse, another suffered a serious neck injury and others were attacked with flares, sticks, snooker balls and smoke bombs.
One student urinated on the Winston Churchill statue in the square, which was also daubed with offensive graffiti, including messages saying “racist warmonger” and “Churchill was a ----”.
A plastic booth thrown on to a bonfire of placards exploded into flames, billowing smoke across Westminster. The riots spread to surrounding areas and several buildings were attacked, including the Treasury, the Supreme Court and Topshop, owned by the billionaire Sir Philip Green.
Scotland Yard condemned the “outrageous and increasing levels of violence”.
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.
“It has gone so far that a car in which the Prince of Wales and the Duchess of Cornwall were travelling through the West End was attacked. Police managed the situation and they were unharmed.” The spokesman said that 20 protesters had been arrested and 38 had been injured.
Sir Paul Stephenson, the Metropolitan Police Commissioner, said he had witnessed at first hand the “violence and disobedience of a number of protesters determined to undermine the peaceful actions of the majority of students seeking to legitimately express their views outside Parliament”.
He commended his officers’ response, saying they had shown “bravery, professionalism and determination to control an extremely challenging situation and maintain peace and order on the streets of the capital.”
A Scotland Yard spokesman said that in the face of “extreme violence” officers had to resort to containing the crowds outside Parliament.
They were repeatedly attacked by surges from a hard core of mask-wearing anarchists and charged back on horseback. Several of the horses were repeatedly struck by missiles, and firecrackers were thrown in attempt to startle the animals.
Some protesters claimed that the presence of mounted police exacerbated an already tense situation.
Footage showed one police officer lying motionless on the ground as he was fitted with a neck brace, after being struck. It is understood his injuries are less serious than first feared and his neck was not broken.
Scuffles began as early as 2pm, ahead of the debate, as tens of thousands of demonstrators marched through London. One officer was seen being dragged to safety by colleagues after being hit on the head in Kingsway.
The controversial policy on raising tuition fees had prompted three resignations from the Coalition Government as two Lib Dems and a Tory stood down as parliamentary aides in order to vote against the proposals.
The Liberal Democrats were split down the middle, with 21 of the party’s 57 MPs rebelling and 27 voting for the proposals. Six, including Simon Hughes, the deputy leader, abstained during the largest revolt of backbench MPs since the party’s formation.
Senior figures, including the former Lib Dem leaders Charles Kennedy and Sir Menzies Campbell, joined forces with respected Conservatives David Davis and Edward Leigh and the Labour Opposition to register their protest against the move to increase the current tuition fee cap of £3,290.
Soon after MPs began their heated five-hour debate ahead of the vote, a group of five protesters was ejected from the public gallery overlooking the Commons chamber after they stood up and began shouting slogans.
Members of the public around them applauded, but the demonstration could not be heard by MPs because of soundproof glass.
As the protests outside grew violent, Conservative MPs were ordered to remain within the parliamentary precincts, to avoid being held up from voting.
Outside, Parliament Square had been blocked off on all sides by up to 1,000 police.
Hundreds of students pushed through the barriers, and flares were lit, as they streamed through metal gates on to the green in the square. As darkness fell, gangs of teenage vandals, some brandishing hammers, formed among the protesters.
About 20 individuals systematically began smashing every pane of glass in each telephone box despite female and male students ordering them to stop. The Supreme Court building was attacked by protesters brandishing shovels, a Christmas tree in Trafalgar Square was set on fire and, at the height of the violence, BBC news reporters were forced to don crash helmets for protection.
Minutes before the vote, Lee Scott, a high-flying Conservative member for Ilford North, announced that he was standing down as parliamentary private secretary to Philip Hammond, the Transport Secretary, in order to take part in the rebellion.
Mike Crockart, a Lib Dem, quit as a parliamentary aide to Michael Moore, the Scotland Secretary, along with Jenny Willott, who performed the same role for Chris Huhne, the Energy Secretary.
Nick Clegg, the Lib Dem Deputy Prime Minister, had hoped to win over doubters by saying that parliamentary private secretaries could stay within the Government if they abstained rather than voted against the tuition fee rise.
But Mr Crockart, the MP for Edinburgh West, said: “I have always believed that access to higher education is the key to narrowing the gap between the richest and poorest in society and I cannot therefore vote for a system which I believe puts barriers in the path of able students.”
Vince Cable, the Business Secretary who drew up the plans, said that he was “proud” of the package he was putting forward.
After the vote, Mr Cable said: “Under our proposals no student will have to pay up front for tuition and both parties in the Coalition have worked hard to develop a much fairer and progressive graduate contribution scheme.
“Graduates will only begin to repay the cost of their tuition and living support once they are in high earning jobs, with significant discounting for those on low and modest incomes.”
Thousands of students also protested in Edinburgh, Newcastle, Belfast, Brighton and Swansea. In Glasgow marchers targeted businesses they claimed were avoiding paying tax to the Treasury.
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