Britain's top mandarin is being urged to investigate who leaked a story claiming that the Queen expressed Eurosceptic views during a private lunch - with Justice Secretary Michael Gove seen as a prime suspect.
Sources told The Sun the monarch vented her anger with Brussels at pro-EU former deputy prime minister Nick Clegg during a Privy Council event at Windsor Castle in 2011.
Buckingham Palace has lodged an official complaint with the Independent Press Standards Organisation (Ipso) and Mr Clegg has branded the claims "untrue". But the newspaper says it stands by the front page story, headlined "Queen Backs Brexit".
In his role as president of the Privy Council, Mr Clegg attended nine meetings of the body at which the Queen was present during 2011, including one at Windsor Castle on April 7.
It is not clear whether this meeting included the lunch reported in The Sun. Privy Council meetings often take place in the late afternoon and do not usually involve a meal.
But a court circular records that the April meeting happened at 12.40pm, leaving open the possibility - which has not been confirmed - that the Queen may have invited her guests to lunch before or after the formal session.
Also present at the April 7 meeting were fellow privy councillors Mr Gove and Cheryl Gillan - both advocates of a vote to leave the EU in the June 23 referendum - as well as Liberal Democrat peer Lord McNally.
Asked whether Mr Gove had any recollection of discussions taking place at that meeting, a spokeswoman for the then education secretary told the Press Association: "We don't comment on private conversations with the Queen."
A spokeswoman for Ms Gillan, who was Welsh secretary at the time, said: "Ms Gillan has no comment to make on Privy Council matters."
Labour MP Wes Streeting has written to Cabinet Secretary Sir Jeremy Heywood urging him to investigate the leak.
Mr Streeting wrote: "If anyone present at the meeting in question were found to have disclosed information about what was discussed it would be an extremely serious breach of the rules of the Privy Council, and this possibility should therefore be thoroughly investigated and acted on accordingly.
"If it is found that none of those who were present at the meeting in questions are implicated, I urge you to establish which 'impeccably placed' individuals were involved in making such allegations to a national newspaper."
The Ilford North MP told the Press Association: "From my reading of the report, I think it is very clear that it is suggested that one or two senior members of the Privy Council - who may or may not still be in the Government - may have been involved, and I think Sir Jeremy has a duty to investigate.
"Whoever has sought to drag the monarch into the referendum debate for their own ends ought to be dragged into public to explain why they behaved in such an inappropriate way, and to apologise."
A senior Downing Street source declined to comment on the report, saying only that the Palace and Mr Clegg had already made statements.
Mr Cameron spoke with Mr Gove on Wednesday morning, but it is understood that their conversation revolved around preparations for Prime Minister's Questions in the Commons, rather than the row over the Queen's alleged comments. The Justice Secretary was not present for the weekly PMQs session.
One Conservative MP backing UK withdrawal from the EU said he was "uneasy" about apparent efforts to use the Queen's supposed opinions to influence the referendum vote.
Conor Burns tweeted: "I'm more than slightly uneasy by attempts to try and drag the Queen into EU debate. Monarch shouldn't be used in divisive political debate."