The BBC apologised to Britain's Queen Elizabeth II on Tuesday after revealing that she raised concerns with a previous government about radical cleric Abu Hamza, who faces extradition to the United States.

In a rare clash between two pillars of British life, the broadcaster said it deeply regretted the breach of confidence after correspondent Frank Gardner reported comments that the monarch made to him.

"This morning on the Today (radio) programme, our correspondent Frank Gardner revealed details of a private conversation which took place some years ago with the queen," a BBC spokesperson said.

"The conversation should have remained private and the BBC and Frank deeply regret this breach of confidence. It was wholly inappropriate.

"Frank is extremely sorry for the embarrassment caused and has apologised to the palace."

The European Court of Human Rights on Monday rejected a final appeal by Egyptian born Abu Hamza and four other terror suspects after a long legal battle.

Abu Hamza, the former imam of the Finsbury Park mosque in north London, was jailed in Britain for seven years in 2006 for inciting followers to murder non-believers.

But Gardner, the BBC's security correspondent, reported that the queen had quizzed the previous government before Hamza's initial arrest in 2004 as to why he was still a free man.

"The queen was pretty upset that there was no way to arrest him, she couldn't understand why," Gardner said.

"This is a conversation we had a little while ago and she did say that she had mentioned to — I don't know which home secretary (interior minister) it was at the time — that was there not some law he had broken?"

Buckingham Palace refused to comment.

Gardner was shot and partly paralysed in 2004 in an Islamist attack in Saudi Arabia, while his cameraman was shot dead.

The queen is the United Kingdom's head of state and has regular meetings with the prime minister, but has traditionally stayed outside politics throughout her 60 years on the throne.