Buckingham Palace has written to the press watchdog to register a complaint over claims that the Queen voiced strong Eurosceptic views during a lunch with the former deputy prime minister.
The Sun said she vented her anger with Brussels at the pro-EU Nick Clegg during a lunch at Windsor Castle in 2011.
A Buckingham Palace spokesman said: "We can confirm that we have this morning written to the chairman of the Independent Press Standards Organisation to register a complaint about the front page story in today's Sun newspaper.
"The complaint relates to Clause One of the Editors' Code of Practice."
Clause 1 in the code relates to accuracy and states: "The press must take care not to publish inaccurate, misleading or distorted information or images, including headlines not supported by the text."
It requires that "significant inaccuracy, misleading statement or distortion must be corrected, promptly and with due prominence, and - where appropriate - an apology published".
The Sun's front page headline read: "Queen backs Brexit" and the paper quoted a ''senior source'' as saying that people who heard their conversation ''were left in no doubt at all about the Queen's views on European integration''.
Former Liberal Democrat leader Mr Clegg dismissed the report as ''nonsense'', while the Palace said: "The Queen remains politically neutral, as she has for 63 years.
''We will not comment on spurious, anonymously sourced claims. The referendum is a matter for the British people to decide.''
The rare move by the Palace illustrates the frustration within the Royal Household at the Queen being drawn into a political row.
This is the first time a complaint has been registered by the Palace about or on behalf of the Queen with Ipso, the independent regulator of the newspaper and magazine industry, which was set up in 2014.
In 2012, Clarence House contacted the Press Complaints Commission (PCC) after mobile phone images of Prince Harry naked in a Las Vegas hotel room were widely circulated online.
In 1999, the Palace made a formal complaint to the PCC about the publication of a topless picture of Sophie Rhys-Jones - now the Countess of Wessex.
Constitutional expert Professor Vernon Bognador told the Press Association it was "absurd" that the Queen would break from her tradition of political impartiality after decades as monarch.
"I'm very dubious. The Queen speaks and acts on the advice of ministers," Prof Bognador said.
He added: "The Queen's been on the throne for over 60 years. She's acted constitutionally throughout. It's absurd to suggest that now she would break from that tradition."