David Cameron today demanded that tuition fee thugs face the "full force of the law" amid calls for an independent inquiry into the mob attack on the Prince of Wales and the Duchess of Cornwall.
But the Prime Minister defended Scotland Yard's handling of the situation, insisting there was no excuse for the "appalling" violence and vandalism.
The son of Pink Floyd frontman Dave Gilmour has apologised after being identified as one of those who climbed on the Cenotaph, the nation's monument to its war dead, as thousands of youngsters vented their fury over MPs' decision to treble university fees to a maximum of £9,000 a year.
Police have so far arrested 33 people as a result of the disorder in central London that left dozens of officers and protesters injured. The Independent Police Complaints Commission (IPCC) has launched a probe into one incident which left 20-year-old student Alfie Meadows requiring brain surgery after allegedly being hit with a truncheon.
Mr Cameron warned that it was not possible to blame the distressing scenes on a small militant element when so many in the crowd were acting in an "absolutely feral way".
"The scenes people saw on their TV screens were completely unacceptable," he said. "I don't think we can go on saying a small minority were there. There were quite a lot of people who were hell bent on violence and destroying property.
"When people see flags being torn off the Cenotaph, when people are despoiling a statue of Winston Churchill, police officers being dragged off police horses and beaten.
"It is not acceptable, it is against the law to smash property, to behave in that way, to attack police officers, and I want to make sure that they feel the full force of the law."
Among the most shocking episodes was the attack on a Rolls-Royce carrying Charles and Camilla by a gang who smashed a window and threw paint while shouting "Off with their heads!".
A Clarence House spokesman refused to confirm reports that the duchess was poked with a stick through an open window, but stressed that the royal couple did not seek medical help.
Metropolitan Police Commissioner Sir Paul Stephenson said an investigation was being held into the security breach, and also said armed protection officers had shown "real restraint" not to open fire as the situation slipped out of control.
"I do think that the officers who were protecting their royal highnesses showed very real restraint - some of those officers were armed.
"Their priority was to get that car to the point of safety, which was the venue, and that was achieved, but it was a hugely shocking incident and there will be a full criminal investigation into it."
Asked whether royal protection officers were allowed to shoot protesters who posed a threat, Sir Paul replied: "I am telling you that there are armed officers who protect principals and they show enormous restraint in achieving that very difficult balance in our society."
Tory backbencher Mark Pritchard insisted there should be an independent probe into why the royal couple were exposed to such danger. "This was an incident that was so very serious - and could have been even more serious - that it should not be left to an internal Metropolitan Police inquiry," he said. "It's not rocket science to know that that part of London would at least be chock-a-block with displaced traffic."
The chaos came weeks after police were criticised for being ill-prepared when tuition fee demonstrators smashed up Conservative Party headquarters in Westminster. But the commissioner stressed that around 2,800 police officers had been deployed yesterday.
"But we were very, very stretched - this was a very large policing operation," he added.
"Whilst the majority did come to demonstrate peacefully, the minority of that majority was a significant number of people who came prepared for violence and clearly demonstrated that violence on police lines.
"We did everything we could to facilitate peaceful protest, everything we could to keep that calm, and the police lines were attacked."
Downing Street said the Prime Minister had "full confidence" in the police.
Charlie Gilmour, son of musician David, could face being questioned by police after he was photographed swinging from the Cenotaph. In a statement, the 20-year-old student expressed his "deepest apologies for the terrible insult to the thousands of people who died bravely for our country" and said he did not realise what the monument was.
"I feel nothing but shame," he added. "My intention was not to attack or defile the Cenotaph. Running along with a crowd of people who had just been violently repelled by the police, I got caught up in the spirit of the moment."
National Union of Students president Aaron Porter stressed that protests should be peaceful, but said young people were "engaging with the issues" over tuition fees.
"Peaceful protest is an integral part of our heritage and it is the responsibility of the police to help facilitate that," he said.
"Throughout this campaign, thousands of young people who have been in the past dismissed as politically apathetic have engaged with the issues and are seeking a way to express their opinions."
Another student leader, Mark Bergfeld of the Education Activist Network, claimed demonstrators suffered "police brutality" and "horrendous" conditions as they were herded and kept in one place for up to 10 hours.