David Cameron’s admission he sought the Queen’s involvement in the Scottish independence referendum has raised questions about the legitimacy of the nation’s constitutional monarchy, an expert has said.

Mike Gordon, professor of constitutional law at the University of Liverpool, said the revelation would be an “awkward and embarrassing” incident for the former prime minister, the monarch and those advising her.

But in the long term, the “viability” of having a hereditary head of state would also come under scrutiny, he said, in light of Mr Cameron’s comments which suggest the Queen appeared to step away from her position above party politics.

Mr Cameron has told a BBC documentary he made contact with Buckingham Palace officials in 2014, suggesting the monarch could “raise an eyebrow” in the closely fought referendum campaign.

A few days before the referendum in September that year, the Queen told a well-wisher in Aberdeenshire that she hoped “people would think very carefully about the future”.

Prof Gordon said: “In a democracy, the whole idea that you have a hereditary, unelected head of state is premised on the idea that she will try and keep herself out of politics and try and be impartial.”

He said when one of her ex-prime ministers reveals he asked for a “subtle political intervention”, then: “The idea the Queen has in some way perhaps acceded to the request by making even a very vague, guarded comment does start to raise all sorts of difficult questions about the legitimacy of the position.”

Prof Gordon added: “The Queen has made major efforts to generate and sustain that image of herself as being above politics and that’s why the revelation from Cameron is particularly damaging or challenging for her because she has tried to position herself as above this.”

The former prime minister’s comments are the latest major constitutional issue involving the Queen – following hard on the heels of Prime Minister Boris Johnson’s controversial advice to the monarch to prorogue Parliament.

Mr Johnson’s decision is the subject of a Supreme Court hearing, with justices asked to determine whether the prorogation move – which has closed down Parliament until October 14 – was unlawful.

The academic said: “It does show when you have tumultuous political times that place real strains on the formalities of a system of monarchy, if we are going to continue living through a tumultuous political period then questions about reform to the role of the monarch and powers of the monarch are only going to intensify.”

Mr Cameron’s discussions of the conversations that have taken place between his office and the Queen’s private secretary have broken the convention of keeping communications between the head of state and prime minister secret.

Prof Gordon said: “These sorts of conventions governing the relationship between the prime minister and the Queen are absolutely central to maintaining a system with an unelected, hereditary monarchy as head of state.

“The Queen acts on the prime minister’s advice but there is that confidential space in which they can have those discussions, and the confidentiality of that space is keenly protected to ensure the continuation of this idea the Queen is politically impartial and above the political fray.”