British Prime Minister David Cameron has apologised to the Queen for letting slip her delight at the result of the Scottish independence referendum.

The Prime Minister was recorded earlier this week discussing the Queen’s reaction with former New York mayor Michael Bloomberg. He told Mr Bloomberg that the Queen “purred down the phone line” when he told her that the ‘no’ side had won the referendum and that the UK would remain intact.

Speaking in New York, Cameron later said that he was mortified that he had breached the protocol that discussions between the Queen and Prime Minister are never made public.

The Daily Mail reports that officials representing the Prime Minister have already been in touch with Buckingham Palace to offer his apologies, but he will also personally apologise when he next meets the Queen face-to-face.

The Prime Minister said: “Look, I’m very embarrassed by this. I’m extremely sorry about it. It was a private conversation, but clearly a private conversation that I should’t have had and won’t have again. My office has already been in touch with the palace to make that clear and I will do so as well.”

Constitutional experts have criticised Cameron’s gaffe, with Dr Andrew Smith of University College London (UCL) saying: “While it doesn’t seem unnatural for the Queen to have an opinion … it was a particularly sensitive phone call telling her that her kingdom was intact.

“It does seem like Cameron has been terribly indiscreet, as if he was playing up [to] the bigger boys.”

“It was very naive not to think there was a chance of the conversation being picked up … given his choice of language, the [description of her] purring and the fact that there is an important constitutional convention here, I have to say it will be the most awkward phone call of his political career,” he added.

However, Professor Robert Hazell, director of UCL’s Constitution Unit, said the gaffe may not be so severe. “[The Prime Minister] had not intended his private remark to Bloomberg to become public. He will be embarrassed … but no lasting damage has been done.”