Cameron was overheard making the remarks to former New York mayor Michael Bloomberg and the quotes were then picked up by several news outlets, including Sky News.

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He reportedly told Bloomberg that the Queen had 'purred down the phone' to him during a telephone call to officially inform her that the UK's union in Scotland remained following a 55% 'No' vote.

According to the BBC, the prime minister is ‘embarrassed’ and ‘extremely sorry’ for the remarks following his telephone conversation with the Queen.

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He told reporters in New York: “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 shouldn’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.”

Downing Street then confirmed that Cameron would apologise to the Queen face-to-face next time he saw her.

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Buckingham Palace has not acknowledged the comments.