Monday's front pages
The Daily Mail is one of many papers to mention Keith Vaz - who is accused of paying for the services of male escorts - on its front page.
It says the Labour MP is "clinging to power", after refusing to resign from his position as chairman of the home affairs select committee. The accusations against Mr Vaz were first reported in the Sunday Mirror.
With the headline "Vaz to leave committee role over sex claims", the Guardian says the Labour MP has conceded he will have to relinquish his post as chair of the Commons home affairs select committee - at least temporarily - after allegations that he hired male escorts.
But it says he seems to be hoping he will not have to give up the role for good.
"Shameless" declares the front of the Daily Mail, above a photo of Keith Vaz with his wife.
It is among several papers to chart difficulties he has survived over the years, describing him as Teflon.
But its editorial says it is now impossible to see how he can stay on as an MP at all.
'Punish junior doctors'
The Daily Mirror says Tory MPs are urging Theresa May to "punish junior doctors" by banning their right to strike.
For the paper, that's a "sick strategy" from what it calls "rattled Tories losing the public argument with hospital doctors".
The Guardian, meanwhile, says the General Medical Council's warning about the potential risks of the strike action is the "bluntest yet".
It believes the regulator's statement contains an implicit threat that doctors who withdraw care could be at risk of sanctions, including possibly being struck off.
A new type of university catches the attention of The Times, with plans to abandon lectures and traditional terms, and be the first to charge fees of £12,000 a year.
The institution in Hereford will specialise in engineering and teach students in teams of no more than 30, setting practical problems in 13 three-week blocks.
For the paper, its genuinely radical ideas could teach traditional universities a lesson.
With the headline "Migration points system will not work, says May", the Times leads with Mrs May rejecting the idea pushed by five cabinet ministers - and promised by the Vote Leave campaign ahead of the referendum.
It says the prime minister has also left open the possibility that EU migrants may have preferential rights to live and work in Britain after Brexit.
"Lose on Points" is the headline for the Sun, which says Mrs May's attack on the Australian-style system is a rebuff to Foreign Secretary Boris Johnson and Vote Leave, and threatens to open up a new cabinet Brexit rift.
The Financial Times believes Mrs May's stance is "poised to inflame Brexit hardliners".
It notes that her comments came as Japan and the US warned investment could flee the country and business ties be damaged unless she negotiates a very "soft" British exit from the EU, which safeguards access to the single market.
The Daily Mirror says Mrs May has also shattered the illusions of pro-Brexit colleagues by admitting Britain could continue to, in its words, "pump cash into the European Union".
"May refuses to guarantee Brexit pledges" is the lead headline for the Guardian, which says the prime minister has cast doubt on whether Brexit will lead to either a points-based immigration system or an extra £100m a week for the NHS.
The paper says her decision not to endorse what it calls "the key planks of the Vote Leave manifesto" may anger people who thought they were voting for firm pledges made by politicians now senior in her government.
"PM could stop Boris's plan for points-based immigration" is the headline for the Daily Telegraph, which says Mrs May is instead considering a work permit system, which would enable Britain to introduce quotas on the numbers of migrants for parts of the economy.
'Difficult times ahead'
The Daily Express takes a different tack.
With the headline "May: no fear over EU exit", it says Theresa May has "poured scorn on Brexit doom mongers" by saying the "reaction of the economy has been better than some have predicted".
But the Financial Times says the PM also warned of "difficult times ahead" - and believes her cautious words reflected concerns in Downing Street that recent data may have raised false hopes that the economy has emerged unscathed from the Brexit vote.
"Sex shame MP told quit now" declares the front of the Daily Mirror, whose sister paper published the original allegations that Labour's Keith Vaz had paid for male escorts.
It says he is facing growing calls to resign, while one Tory MP has asked for a police investigation.
The paper says the man it calls the "Teflon MP" has "come badly unstuck".
The Times reports that Mr Vaz is facing an investigation by what it calls "parliament's sleaze watchdog" and has signalled privately that he will step aside as chairman of the home affairs committee, either temporarily or permanently.
But the paper describes Mr Vaz as "the great survivor of Labour politics" and "a veteran of parliamentary scandals" and says he started his fight-back by appointing a celebrity lawyer, showing he is "determined to tough it out".
The Sun says Mr Vaz is understood to have told friends he believes he can keep his role by handing over control temporarily and returning when the scandal washes over.
The paper also examines what it describes as "the rise and fall of a political Houdini" over 30 years, but, in its editorial, says this "ought to be fatal for his future as an MP".