Charlie Gilmour, 21, was pictured dangling from the national Union Flag on the Cenotaph memorial during protests on Thursday against a rise in university tuition fees.
The stepson of Pink Floyd guitarist David Gilmour was arrested by police on Sunday for swinging from a flag on London's memorial to war dead during riots last week, British media reported.
Charlie Gilmour, 21, was pictured dangling from the national Union Flag on the Cenotaph memorial during protests on Thursday against a rise in university tuition fees. He later apologised, saying he was ashamed.
"On the morning of Sunday December 12, a 21-year-old man was arrested at his home address in Sussex," police said in a statement. A spokesperson declined to confirm the man's identity.
"He was arrested by officers on suspicion of violent disorder, and attempted criminal damage of the Union Flag, on the Cenotaph on December 9," the statement added, saying he had also been arrested on suspicion of theft.
Gilmour's arrest came as home secretary (interior minister) Theresa May said police must review how they dealt with protests and could use water cannon after last week's disorder.
May confirmed that prince Charles' wife Camilla had come into "contact" with protesters who attacked the couple's limousine as they drove through central London.
Their car was kicked, a window cracked and white paint thrown over it. Media reports said Camilla was poked with a stick through an open window.
"I'm not sure about the term poked with a stick, I understand there was some contact made," May told Sky News.
"I very much regret the incident with the royal car but we have to actually look at how the decisions were taken, what decisions were taken and whether there is something that can be learnt from that."
Thursday's riots followed three other violent demonstrations in London in the past month.
The Metropolitan Police was criticised for failing to stop protesters attacking Millbank Tower, home to the headquarters of the Conservative Party, during the first protest, while students argue the police's "kettling" containment tactic is provocative.
"Whether or not they choose to use water cannon is an operational issue," said May who will be making a statement to Parliament on Monday about the events. "I think it is right we look across the board at all the options that are available.
"We've had a tradition in this country about the way that we police demonstrations like this which tends to be different from the approach that is taken in many other countries."
Ed Balls, Labour's home affairs spokesperson, said it would be dangerous for police to escalate their response.
"I'd say I'm very sceptical about the use of water cannon or rubber bullets because every time in the past you then have a minority who seek to force the police to use that kind of technique," he told Sky News.
Police have arrested some 175 people in connection with the four protests and May said those who committed criminal acts should "feel the full force of the law on them".
"We want the public to help us identify these people who may have been involved in violent disorder, attacking police officers and smashing buildings, shops and windows," said detective chief superintendent Matthew Horne.
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