Charlie Gilmour, son of Pink Floyd guitarist David Gilmour, has been arrested in connection with Thursday's tuition fees protests.
Police said a 21-year-old Sussex man was arrested on suspicion of violent disorder and attempted criminal damage.
He was accused of trying to damage the Union flag on London's Cenotaph.
Mr Gilmour, a Cambridge University student, apologised on Friday for his actions, saying he was "mortified by his moment of idiocy".
The rock stars's adopted son became the 35th person to be held following the violence on Thursday.
Photos of him swinging from a flag appeared on the front pages of many newspapers after the demonstrations.
Mr Gilmour said in a statement: "I would like to express my deepest apologies for the terrible insult to the thousands of people who died bravely for our country that my actions represented."
Just before 1500GMT a 17-year-old man handed himself in at a central London police station and was arrested on suspicion of violent disorder.
Overnight the police have issued images of 14 alleged rioters.
Officers have reviewed hours of CCTV footage as part of their investigations into the disorder and have appealed for the public's help in identifying suspects.
Detective Chief Superintendent Matthew Horne said: "The vast majority of the people we are seeking are suspected of committing serious offences of violent disorder and criminal damage."
Scotland Yard has launched a "major criminal investigation", called Operation Malone, into all the tuition fee protests held from 10 November, when students stormed Tory headquarters in Millbank, up to Thursday's demonstration in Parliament Square.
A total of 177 people were arrested during the four demonstrations, including 34 who were detained on Thursday, Mr Gilmour and the 17-year-old.