Nicola Sturgeon, Scotland’s first minister, has implied the Queen should refuse to be drawn into a future vote on Scottish independence after David Cameron admitted he asked the monarch to intervene in 2014.

Cameron confirmed in a BBC interview he had asked the royal household whether the Queen could “raise an eyebrow” about independence after an opinion poll put support for leaving the UK at 52% a few days before the referendum in September 2014.

The monarch is supposed to be impartial but on the Sunday before the vote she told a well-wisher outside Crathie church near Balmoral: “Well, I hope people will think very carefully about the future.”

Patrick Harvie, the co-leader of the pro-independence Scottish Green party, asked Sturgeon on Thursday whether the UK government could be trusted not to again seek the Queen’s help if a second independence referendum takes place.

“Another referendum is coming, we all know that,” Harvie said during first minister’s questions. “Does the first minister think that we can trust that the head of state won’t once again be invited to interfere in the vote of a sovereign people?”

Sturgeon replied that Scotland’s future “should always be a matter for the Scottish people”, and said support for independence and demand for another referendum was rising.

She added: “Scotland does have a right to choose its own future and I think the revelations, if I can call them that from David Cameron today, say more about him than anybody else, and really demonstrate the panic that was at the heart of the UK government in the run-up to the independence referendum five years ago.

“Of course that is nothing compared to the panic that is in the heart of unionist parties now about independence.” Anti-independence parties have refused to sanction a second vote, while some unionist politicians have floated a leave or remain option in a referendum.

Sturgeon concluded: “They know they do not have the arguments against independence and they know that when Scotland is given the right to choose, Scotland this time will choose to become independent.”

Cameron told the BBC that a YouGov poll putting the yes vote at 52% hit him “like a blow to the solar plexus” and led to “a mounting sense of panic”. He remembered a conversation with Sir Jeremy Heywood, the then cabinet secretary, who in turn spoke to Sir Christopher Geidt, the Queen’s private secretary at the time. Cameron said he was “not asking for anything that would be in any way improper or unconstitutional, but just a raising of the eyebrow, even you know a quarter of an inch, we thought would make a difference.”

A source in the royal household told the BBC there was displeasure at Buckingham palace at Cameron’s disclosures.

The source said “it serves no-one’s interests” for conversations between a prime minister and the Queen to be made public. “It makes it very hard for the relationship to thrive,” the BBC quoted the source as saying.

Cameron was challenged about the Queen’s irritation on the BBC’s Jeremy Vine show, and admitted he may have said too much.

But he said he had been trying to be honest. “I was trying to explain the frustrations there were when you had one side in the referendum saying we’re going to have a Queen of an independent Scotland and everybody is fine and dandy,” he said.