Britain's Prime Minister David Cameron has been overheard describing his nervousness about the Scotland referendum and how Queen Elizabeth II appeared relieved when he called to tell her the result.

The leader was being filmed chatting with former New York Mayor Michael Bloomberg in New York when microphones picked up what they said. The video showing the conversation was broadcast Tuesday on Sky News.

Cameron was heard describing how the queen "purred down the line" after he called to tell her "it's all right, it's OK" after Thursday's referendum, in which Scots rejected independence and chose to stay with the United Kingdom.

"It should never have been that close. It wasn't in the end," he told Bloomberg. "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, you know. It was very nervous."

A spokesman from Buckingham Palace said it never comments on exchanges between the prime minister and the queen.

The queen is prohibited from taking sides in political debates and rarely makes her personal views public. For that reason, she surprised many when she told well-wishers before the referendum that Scots should think "very carefully about the future" before voting.

Following the vote, the monarch said in a statement "all of us throughout the United Kingdom will respect" the poll's result, and that mutual understanding will overcome the "strong feelings and contrasting emotions" during the Scottish debate.