The headline in the Mail on Sunday is "40% of Tory Councillors Back Farage".
A survey in the paper suggests what it calls "an astonishing" number of councillors will support Nigel Farage's new Brexit Party in the European elections. Just over half - 52% - say they will back the Conservatives and 8% other parties.
The poll also reveals that three-quarters of Tory councillors want Mrs May to resign and 96% believe the Tory party has been damaged by the Brexit impasse.
The survey was carried out by Survation, which questioned 781 Conservative councillors last week.
Writing in the Observer, Labour's deputy leader Tom Watson warns that the party will lose out to what he calls the "far right" Brexit Party in the European elections - if it gives the impression it agrees with Mr Farage on Brexit and does not back another referendum.
He stresses that Mr Farage is a real threat to both the Conservatives and Labour - and calls on his own party to offer a radical alternative, which demonstrates his party has a way forward out of the crisis.
The paper says his comments reflect the frustration among senior Labour Remainers about Jeremy Corbyn's lukewarm support for a second referendum.
HS2 'expensive extravagance'
The Sunday Telegraph says Tory voters want the next leader of the party to scrap HS2.
It quotes a briefing produced by the US pollster Frank Luntz, which states that many Conservative supporters are "repulsed" by the high-speed rail project and view the £56bn scheme as an "expensive extravagance".
The paper claims what it calls the "bombshell memo" has been seen by several potential leadership candidates - and adds that Boris Johnson publicly attacked HS2 after being shown the data.
In what it labels an exclusive, the Sunday Times says it can reveal that plans have been drawn up for the Duke and Duchess of Sussex to take on a major international role - which could involve them moving abroad after the birth of their child.
It claims Prince Harry's advisers are working on the couple taking up what it calls "a bespoke" position, probably in Africa, which would combine work on behalf of the Commonwealth, along with charity work, and a role promoting Britain.
The paper says the African scheme took shape after a proposal to make Harry governor-general of Australia or Canada was dismissed as impractical.
Finally, many papers report on the confirmation that Adele has separated from her husband after three years of marriage.
The Telegraph headline is "Queen of break-up ballads to divorce". It adds that the hugely successful singer, who is known for her songs about failed relationships, is now reported to be back in the studio.
The Sunday Mirror says the pair are set for divorce talks, which may see Simon Konecki entitled to part of Adele's £140m fortune.
While he preferred life in England, she loved being with celebrity friends in Los Angeles, according to the Sunday Express.
The Sun on Sunday says record label bosses and Adele's fans can now look forward to an album of "sheer, unadulterated misery" from what it calls the "lyrically gifted genius".