David Cameron has spoken of the relief he felt at not having to tell the Queen that Scotland had left the United Kingdom.

Speaking to businessmen during a visit to New York, the Prime Minister made clear that he had been dreading the prospect of having to inform her that Scotland had voted Yes to independence in last week's referendum.

He smiled broadly as he recalled how he was able to tell her it was "all right" after the referendum resulted in a victory for the No camp.

Mr Cameron said: "The definition of relief, if you are Prime Minister of the United Kingdom, is ringing up Her Majesty the Queen and saying 'Your Majesty, it is all right, your kingdom is still united'. That's relief."

However, Cameron was also caught on camera claiming the Queen "purred" down the line after he informed her Scotland had not voted for independence.

The Prime Minister was heard telling former New York mayor Michael Bloomberg of the relief he felt at not having to inform the Queen that Scotland had left the United Kingdom.

He smiled broadly as he recalled how he was able to tell her it was "all right" after the referendum resulted in a victory for the No camp.

Mr Cameron said: "The definition of relief, if you are Prime Minister of the United Kingdom, is ringing up Her Majesty the Queen and saying 'Your Majesty, it is all right, it's okay. That was something.

"She purred down the line."

He added: "But it should never have been that close. It wasn't in the end.

"But there was a time in the middle of the campaign when it felt..."

Mr Bloomberg spoke before Mr Cameron finished his sentence in a period of the recording which is inaudible.

The PM went on: "I've said I want to find these polling companies and I want to sue them for my stomach ulcers because of what they put me through. It was very nervous moments."