The Prince of Wales and his wife Camilla, Duchess of Cornwall, reacted with shock as their car was attacked by rampaging students during last night's tuition fees protest in London.

Angry demonstrators targeted the couple as they were driven along Regent Street towards the London Palladium for the annual Royal Variety Performance. Charles and Camilla were seen joking in the foyer with acts including Take That, Kylie Minogue and N-Dubz. Their Rolls-Royce limousine, which had cracked windows and a large white paint stain on a rear panel, was left parked outside.

A witness said the vehicle became separated from its police escort near Oxford Circus and was surrounded by protesters leaving Trafalgar Square. Bottles and dustbins thrown by the crowd struck the limo, and another car carrying members of the royal staff had its windows smashed. Camilla was noticeably shaken. After the variety performance, members of the Royal Family usually meet the entertainers backstage to thank them for their efforts – but Charles and Camilla left minutes after Take That closed the show. When asked how she was as she left, the Duchess said: "I'm fine thanks – first time for everything." Charles, following behind, smiled as they got into a police van which took them away.

Prime Minister David Cameron said it was "shocking and regrettable" that the royal car was attacked and that violent protesters must face the "full force of the law". Sir Paul Stephenson, the commissioner of the Metropolitan Police, said it was a "disappointing day for London" and promised a full investigation into the day's disturbances.