During the St Paul’s Cathedral event, he was seen standing silently, a few places away from Prime Minister David Cameron, as those around him sang along.
Last night Tory MP Sir Nicholas Soames, the grandson of Winston Churchill, said not singing the anthem was “very rude and very disrespectful” to the Queen and “the Battle of Britain pilots who gave their all”.
Sir Nicholas said: “It was an extremely disrespectful thing and I think he needs to make his mind up whether he is a grown-up or not.”
Ukip leader Nigel Farage, who was also at the service, described Mr Corbyn as a “hardcore republican”.
Mr Corbyn has in the past called for the monarchy to be abolished but since winning the Labour leadership election in a landslide at the weekend, he has accepted becoming a member of the Queen’s privy council. Mr Rosindell, MP for Romford, offered to teach Mr Corbyn the words to the national anthem.
He said: “I congratulate Jeremy on his success and he is a man of principle, he has strongly held views and I respect him for that.
“However, I hope that now he is leader of Her Majesty’s Opposition and leader of the Labour Party he will understand that the British people are overwhelmingly supportive of our monarchy and our constitution.
He said Mr Corbyn was free “not to do it in private” but he should sing the anthem when attending a “state occasion”.
Ahead of the event, Mr Corbyn highlighted that his mother had served as an air raid warden and his father in the Home Guard.
He said: “Like that whole generation, they showed tremendous courage and determination to defeat fascism. The heroism of the RAF in the Battle of Britain is something to which we all owe an enormous debt of gratitude.”
After the service, Mr Corbyn and deputy Tom Watson left and stopped to talk to workers from high street coffee shop chain Costa. Mr Corbyn posed with the staff as Mr Watson took a picture with a smartphone.