The son of Pink Floyd guitarist David Gilmour could be questioned by police after he admitted swinging from a Union Flag on the Cenotaph during the student protests.
Charlie Gilmour, 21, apologised for climbing on the memorial to Britain's war dead in Whitehall, central London, saying he was "mortified" by his "moment of idiocy".
The Cambridge University history student said he did not realise it was the Cenotaph and felt "deeply ashamed" by his actions during Thursday's demonstration against higher tuition fees.
He only realised the significance of his actions after seeing pictures of himself in newspapers hanging from the flag with his legs dangling, a source said.
Scotland Yard said a 19-year-old man was held on Thursday night on suspicion of causing criminal damage in relation to the Cenotaph incident.
It is understood that this was not Mr Gilmour and there could be further arrests as the investigation progresses.
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.
"I feel nothing but shame. 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.
"I did not realise that it was the Cenotaph and if I had, I certainly would not have done what I did.
"I feel additionally mortified that my moment of idiocy has distracted so much from the message the protest was trying to send out."