CBS News correspondent Elizabeth Palmer reports that some of the student demonstrators shouted "off with their heads," smashed a window, and splattered the royals' car with paint.
The prince's police escort quickly came to the rescue and the couple - unharmed, but clearly shocked - arrived safely at a gala variety show in central London.
Charles and Camilla put a brave face on as they emerged from the car, quickly picking up their ceremonial duties and shaking hands with a few well wishers before heading into the theater.
"They were whisked right through to hospitality where Camilla had a rather stiff brandy to calm her nerves," reveals CBS News contributor Neil Sean, who reports frequently on the royal family and attended the Royal Variety Show.
VIDEO: Report from London
Police say the prince's car, and his security detail, were caught off guard by a fast-moving group of protesters who converged on the area of the theater at short notice.
Regardless of where they came from and how long they had been there, the violent group's ability to come within inches of the man next in line to sit on the throne will doubtless prompt a review of security plans for the wedding of Charles' son, Prince William, being planned for this summer.
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Earlier Thursday, thousands of students demonstrated in central London against a government move to enable the country's universities to triple tuition fees - to 14,000 dollars per year.
Sporadic pushing and shoving with the police gradually escalated, with officers on horseback brought in to break up the crowds.
As night fell, it turned violent. Some demonstrators lit fires, others attacked government buildings.
But it's the attack on the royal car that's grabbing the headlines this morning.
Metropolitan Police Commissioner Sir Paul Stephenson called the attack, "a thoroughly disgraceful incident," and he vowed there would be "a very full and detailed criminal enquiry into how that attack happened."
For the trip home from the royal gala, Prince Charles and his wife travelled in an armored police van.