David Cameron is "petrified" of Boris Johnson and branded Michael Gove a "Maoist" who wants to be the darling of the Tory right, according to an insider's account of the Coalition years.
The Prime Minister is said to have confided in Nick Clegg that the Justice Secretary had "gone a bit nuts recently" and was driving him "around the bend".
Mr Cameron also admitted to the former deputy prime minister that the London mayor "is clearly after my job", the memoirs of former Liberal Democrat Cabinet minister David Laws claim.
Extracts published in the Mail on Sunday also state the premier agreed to a referendum to keep his "mad" backbenchers happy.
But the book, which has been written with Mr Clegg's cooperation, is also likely to open the former Lib Dem leader up to criticism after he sets out details of a conversation with the Queen.
Mr Clegg was critical of attempts to "drag the Queen" into the referendum campaign after comments she was alleged to have made about the EU were leaked to a newspaper.
The Justice Secretary, who has been accused of being the source, had a publicly fractious relationship with Mr Clegg but has long been a close friend of the Prime Minister.
But the book, Coalition: The Inside Story Of The Conservative-Liberal Democrat Coalition Government, suggests the relationship may have been under strain in recent years.
Setting out details of a conversation between the PM and his deputy about Mr Gove, the book states: "Cameron replied to the Deputy Prime Minister's complaints about Gove by saying 'Look, I understand your frustration over this, Nick. Michael does seem to have gone a bit nuts recently. To be honest, I am being driven around the bend by Michael right now. We know he isn't very popular in the country.'
"When Nick complained again after another bust-up with Gove, the Prime Minister laughed. 'The thing that you've got to remember with Michael is that he is basically a bit of a Maoist - he believes that the world makes progress through a process of creative destruction!'"
Mr Gove, meanwhile, told a private meeting of Tory and Lib Dem ministers that the PM's referendum was "completely barmy", according to Mr Laws.
Mr Clegg gave the former minister, a close ally, open access to his private papers and diaries, according to the Mail on Sunday.
"'God, Osborne and Cameron really are desperate for power, aren't they?' Nick Clegg told me in his cavernous office at 70 Whitehall, with its extensive views of Horse Guards' Parade, on March 29, 2012," Mr Laws recounts.
"They would sell their mothers to stay in Downing Street. They are petrified of Boris Johnson coming along and challenging them for the leadership."
The book reveals details of a joke the Queen is said to have made to Mr Clegg who, as Lord President of the Privy Council, was at Buckingham Palace in 2012 for a regular audience.
"'What is happening in Parliament at the moment?' asked the Queen. Nick Clegg shifted uncomfortably. 'Well, Ma'am' he said, 'I am not sure that you are going to approve. We are just legislating to change the rules on the Royal succession. For the first time ever in the history of the British monarchy, a first-born girl will succeed to the throne before a later-born boy'.
"The Queen was quiet, staring off into the middle distance. 'I hope this change does not cause difficulties, Ma'am?' added the Deputy Prime Minister, to break the silence. 'Good grief, Mr Clegg', the Queen said, turning her face back again. 'By then, I'll be dead!'"
Mr Cameron is reported to have compared the fallout from his decision to push ahead with gay marriage to the impact the U-turn on tuition fees had on the Lib Dems.
"Over food and wine in the 10 Downing Street flat, the prime minister told Nick Clegg: 'Gay marriage has been an absolute disaster. It has totally split my party. It has been as bad for me as tuition fees were for you, Nick'. The prime minister said he now realised that it had been a big mistake to upset the 'Tory base' in the country."
Mr Laws told how he got "nervous" in the run-up to the 2015 Budget "when it became clear Osborne's proposal to completely abolish the tax on savings income may cost far more than his £800 million estimate".
"I said it was wrong when there were also painful cuts to the incomes of the poorest. Even Osborne admitted it wasn't well targeted. 'It will only really be of help to stupid, affluent and lazy people, who can't be bothered to put their savings away into tax-efficient vehicles! But it will still be very popular - we have polled it'."