The royal family is seriously considering making a dramatic intervention in the referendum debate with an announcement that it supports Britain remaining inside the European Union.

That the royals are prepared to risk provoking a potential constitutional crisis shows just how deep their anger is at parts of the British press and senior politicians.

According to a senior source close to official figures, there was particular resentment at the Sun’s newspaper’s depiction of the Queen as a Brexit supporter.

But the anger runs through the generations at Buckingham Palace: there was fury at the claims about “workshy” Prince William, a campaign mounted by two papers with an anti-EU stance, the Daily Mail and the Sun. And there was a feeling last week that rock bottom had been hit with a story in the Mail that Kate was now posher than the other royals.

Using outside experts who advised that the intervention would need to be presented by a figure with impeccable European credentials, a strong affinity with the continent and the character to speak out, the family has decided that the move should fronted by Prince Philip.

Prince Philip: ‘impeccable European credentials’ Photograph: Murdo Macleod/The Guardian

“He has been hugely impressed by the way the EU stepped in, not just once but several times, to save Greece,” said one official with knowledge of events. “He admires what Tsipras and Varoufakis achieved – in fact he told friends he sees something of his younger self in the charismatic, motorbike-riding, eye-for-the-ladies Varoufakis. Mind you,” added the source, “he also thinks the Greeks would never have got into this mess if the colonels had still been in power.”

Another well-connected source explained that the royals now see a tightening conspiracy between the pro-exit papers, notably the Sun, Telegraph and Mail, and certain politicians. “The leader of Vote Leave is Michael Gove – that awful little leaker who put it about that the Queen wanted out. They can’t stand him. And as for Boris, the other main outer – he’s a cycling maniac from Islington. All he has done for the royal family is make it difficult to get around London in a decent-sized Daimler. And the third of the trio – Farage – what another awful little man.”

Part of the reason for stepping into the debate in such an unprecedented way is huge disappointment in the prime minister, David Cameron.

We can’t leave it to Cameron. Look what happened with the Scottish referendum. It was a damn close-run thing Royal source

“The feeling is that we can’t leave it to him. Look what happened at the last referendum we had, on Scotland. We nearly lost Balmoral and the shoots. Nicola Sturgeon could be sat in that castle now – we know she had her eye on it – it was a damn close-run thing.”

Royal circles found particularly offensive Cameron’s portrayal of the Queen as having “purred down the line” when he telephoned her to tell her Scotland had voted against independence. “The cheek of the man. There was real fury about that comment. And the irony of it – coming from a fat cat,” said a source.

Remaining questions of strategy are being resolved by an inner circle at the palace. On timing, the date picked for Philip to make a nationwide address is 10 June, crucially just two weeks before the referendum on 23 June. Courtiers have noted the added poignancy of 10 June – it is Philip’s 95th birthday.

On which platform to use, the source said: “We want to avoid that ‘bloody little man’, as Charles called BBC royal reporter Nicholas Witchell.”

Kensington Palace sources say the choice is a tight one between ITV’s news anchor Tom Bradby, who is preferred by Prince William, and Prince Harry’s strong favourites Ant and Dec. Harry argues that the Saturday Night Takeaway presenters would reach a different demographic and be particularly appealing to “people in the north with accents”.

“William says that chap at ITV, Bradby, sees things like us. And there is a strong feeling that we should do over the Bleating Broadcasting Corporation. Serve them right for cocking up the Queen’s water pageant with those disc jockeys instead of using a Dimbleby.”

Another insider said early proposals to do a live broadcast have been rejected in favour of a pre-recorded session because of Philip’s propensity for swearing. “The words have to be perfect,” she said, “but we’ve got time to iron things out between today – 1 April – and June.”