The protest was in response to rising tuition fees at British universities.
Gilmour was photographed climbing atop The Cenotaph - of one of Britain's most important war memorials – and swinging from the Union Jack.
The BBC reports police said the 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.
The rock star's adopted son became the 35th person to be held following the violence on Thursday. A total of 176 people were arrested during the four demonstrations, including 34 who were detained on Thursday, and Mr Gilmour.
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."
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