An "explosive book" by former Prime Minister David Cameron's communications director Sir Craig Oliver makes the front page of the Mail on Sunday.
For the paper, the revelations about Mrs May are are at odds with her "reputation for straight-talking".
It says Foreign Secretary Boris Johnson "fares equally badly" from what it calls his "secret last-minute wobble about leaving the EU".
A second book on Brexit is featured on the front page of the Sunday Times, under the headline "Cameron's 'lily-livered' sneer at May".
The headline is based on revelations about the referendum campaign in a book by the paper's own political editor, Tim Shipman.
Aides to Mr Cameron reveal he made the "lily-livered" remark about Mrs May and the then foreign secretary, Philip Hammond, after they failed to support his plans to push for an "emergency brake" to limit the number of EU migrants coming to Britain.
The paper says they did not support the prime minister because Germany did not approve the measure.
However, in its editorial, the Sunday Times says Mr Cameron "has only himself to blame" for the referendum result.
It argues he was "a confident prime minister at home" but "lacked a sure touch abroad".
The Sunday Telegraph, meanwhile, says it has learnt that Mr Cameron and his former cabinet colleague Michael Gove have not spoken since the Brexit vote.
It is a sign, it says, that the referendum has destroyed one of the most powerful friendships in politics.
There is widespread coverage of the Labour leadership result and the re-election of Jeremy Corbyn in all the papers.
The shadow chancellor, John McDonnell, tells the paper it's now up to the leadership to show they would listen to the concerns of all those in the parliamentary party - and insists there are no plans for a purge.
But the paper's editorial concludes that an uncomfortable truce seems the best the party can hope for. It says a mutually assured destruction remains a real danger.
With the headline "Left out", the Sun on Sunday says Labour faces a mass exodus of MPs. The paper believes Mr Corbyn's victory was "electoral suicide" for Labour.
The Sunday Mirror's headline, meanwhile, is Mr Corbyn promising: "I'll win over rebel MPs".
However, a poll for the paper suggests only 16% of the electorate think Mr Corbyn can win the next election. In what it describes as "a massive thumbs down", only 37% of Labour supporters think success is possible.
The Sunday Times columnist, Adam Boulton, says the party's MPs are vying with the Turkish military for the prize "most botched coup", with the target of their insurrection having ended up more entrenched in power.
Andrew Roberts of the Telegraph agrees. The catastrophe that has engulfed Labour is, he argues, "entirely self-inflicted".
London mayor, Sadiq Khan, tells the Sunday Times his party risks extinction unless Mr Corbyn drops what he calls plans to "take revenge on his critics".
The paper believes Mr Corbyn's victory on Saturday has plunged his party into a dark age.
According to its editorial, Mr Corbyn and his allies are "grizzled relics of a narrow and failed political past, not a bright new future."
Meanwhile, writing in the Sunday Telegraph, the Labour former cabinet minister, Yvette Cooper, reveals she has been subjected to online death threats.
Ms Cooper believes that - although not from a party member - the threat illustrates the growing problem of abuse Mr Corbyn must address.
It may not quite be the end of the soggy bottom, according to the Sunday Times.
It says the BBC is planning to rush out a new baking show starring Mary Berry, Mel Giedroyc and Sue Perkins, before Channel 4 is able to air its version.
Channel 4 poached Bake Off from the BBC this month but may not be able to screen the show until summer 2018, leaving time for a rival to be rushed out, it says.
The Sun, meanwhile, says sources have revealed "blundering Channel 4 bosses" agreed to pay £75m for the Great British Bake Off without first asking if the programme's stars were on board.
The Daily Star Sunday reports that one of the favourites to present the new Channel 4 show, Clare Balding, has said she "wouldn't be remotely interested" in the job.
And finally, the Telegraph introduces its readers to two of the new secret weapons being used to attract visitors to stately homes - cats.
Forget the antiquities, it says, growing numbers are being enticed to visit stately homes by the prospect of spotting what it calls "aristocats".
It features cats called Craig and Committee, of Gunby Hall, in Lincolnshire.
The moggies are, it says, among several who have become social media sensations, leaving younger visitors desperate to meet them in real life.