BBC journalist Frank Gardner has apologised for a "breach of confidence" after telling Radio 4's Today programme that the Queen had voiced concerns about the UK's inability to arrest Abu Hamza.
The reporter recounted a conversation with the monarch where she said she had previously raised the issue with a senior Cabinet minister.
A BBC spokesman said: "This morning on the Today programme our correspondent Frank Gardner revealed details of a private conversation which took place some years ago with The Queen.
"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."
Gardner, the BBC's security correspondent, had told the radio programme: "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 it was at the time - that was there not some law he had broken?
"I wouldn't say she was necessarily lobbying, that's not for me to say, but like anybody she was upset that her country and her subjects had been denigrated by this man who was using this country as a platform for his very violent, hateful views."
A Buckingham Palace spokesman declined to comment.
On Monday, Hamza and four other terror suspects were told they could be put on a plane to the United States within days after Europe's human rights judges rejected their bid for an appeal.
A panel of five judges threw out their request to the Grand Chamber of the European Court of Human Rights, clearing the way for extradition.
Hamza, who was jailed for seven years for soliciting to murder and inciting racial hatred, has been fighting extradition since 2004.