David Cameron has revealed the Queen welcomed the news that Scotland would remain part of the UK, saying the monarch "purred down the phone".

The prime minister indiscrete remarks, made to former New York mayor Michael Bloomberg, were overheard by a Sky News camera crew as the duo walked through an office in the Big Apple.

Recalling his phone conversation with Her Majesty following the 55% No victory, Cameron told Bloomberg: "The definition of relief is being the prime minister of the United Kingdom and ringing the Queen and saying: 'It's alright, it's OK.' That was something. She purred down the line."

Although part of their exchange is inaudible, he is then heard saying: "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..."

It is the first time Cameron has been heard discussing his interactions with the Queen. Although he was unwittingly recorded, his revelations are likely to raise questions about the royal's neutrality.

Throughout the campaign she only addressed the referendum question once when she told a well-wisher outside church that she hoped voters would "think very carefully" about the future.

Ahead of the vote, Buckingham Palace insisted that Her Majesty remained unbiased.

"Any suggestion that the Queen would wish to influence the outcome of the current referendum campaign is categorically wrong. Her Majesty is simply of the view that this is a matter for the people of Scotland," a spokesperson said in a statement.

Scotland last week voted against independence, with 55 per cent voting "No" to 45 per cent voting "Yes".

Cameron who is in New York for a UN general assembly meeting, has since joked that he found it insulting that some pollsters has suggested the two campaigns were neck and neck.

He reportedly said: "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. [They were] very nervous moments."