A senior Labour figure has stamped on talk of an early deal with Theresa May to rescue Brexit, warning her proposals would see private US health giants “getting their hands” on the NHS.

Jonathan Ashworth, the shadow health secretary, said ministers “haven’t really shifted” in the long-running negotiations – despite speculation that a cross-party agreement could be struck as early as this week.

He criticised Tory “spin doctors” for briefing that a deal was close, saying: “The problem is that, although the government is trying to redress their customs union offer, they haven’t really shifted.”

The Tories were still seeking to “do their own trade deals” in services, Mr Ashworth warned, adding: “With the United States, that could mean Trump’s America and big private healthcare corporations getting their hands on NHS contracts.”

“I’m not prepared to countenance that – it’s why we need instead a permanent and comprehensive customs union arrangement,” he said, adding: “Our NHS mustn’t be for sale.”

Put It To The People march: Best of The Independent’s pictures Show all 24 1 /24 Put It To The People march: Best of The Independent’s pictures Put It To The People march: Best of The Independent’s pictures Put It To The People protest 23 March 2019 Angela Christofilou/The Independent Angela Christofilou/The Independent Put It To The People march: Best of The Independent’s pictures Put It To The People protest 23 March 2019 Angela Christofilou/The Independent Angela Christofilou/The Independent Put It To The People march: Best of The Independent’s pictures Put It To The People protest 23 March 2019 Angela Christofilou/The Independent Angela Christofilou/The Independent Put It To The People march: Best of The Independent’s pictures Put It To The People protest 23 March 2019 Angela Christofilou/The Independent Angela Christofilou/The Independent Put It To The People march: Best of The Independent’s pictures Put It To The People protest 23 March 2019 Angela Christofilou/The Independent Angela Christofilou/The Independent Put It To The People march: Best of The Independent’s pictures Put It To The People protest 23 March 2019 Angela Christofilou/The Independent Angela Christofilou/The Independent Put It To The People march: Best of The Independent’s pictures Put It To The People protest 23 March 2019 Angela Christofilou/The Independent Angela Christofilou/The Independent Put It To The People march: Best of The Independent’s pictures Put It To The People protest 23 March 2019 Angela Christofilou/The Independent Angela Christofilou/The Independent Put It To The People march: Best of The Independent’s pictures Put It To The People protest 23 March 2019 Angela Christofilou/The Independent Angela Christofilou/The Independent Put It To The People march: Best of The Independent’s pictures Put It To The People protest 23 March 2019 Angela Christofilou/The Independent Angela Christofilou/The Independent Put It To The People march: Best of The Independent’s pictures Put It To The People protest 23 March 2019 Angela Christofilou/The Independent Angela Christofilou/The Independent Put It To The People march: Best of The Independent’s pictures Put It To The People protest 23 March 2019 Angela Christofilou/The Independent Angela Christofilou/The Independent Put It To The People march: Best of The Independent’s pictures Put It To The People protest 23 March 2019 Angela Christofilou/The Independent Angela Christofilou/The Independent Put It To The People march: Best of The Independent’s pictures Put It To The People protest 23 March 2019 Angela Christofilou/The Independent Angela Christofilou/The Independent Put It To The People march: Best of The Independent’s pictures Put It To The People protest 23 March 2019 Angela Christofilou/The Independent Angela Christofilou/The Independent Put It To The People march: Best of The Independent’s pictures Put It To The People protest 23 March 2019 Angela Christofilou/The Independent Angela Christofilou/The Independent Put It To The People march: Best of The Independent’s pictures Put It To The People protest 23 March 2019 Angela Christofilou/The Independent Angela Christofilou/The Independent Put It To The People march: Best of The Independent’s pictures Put It To The People protest 23 March 2019 Angela Christofilou/The Independent Angela Christofilou/The Independent Put It To The People march: Best of The Independent’s pictures Put It To The People protest 23 March 2019 Angela Christofilou/The Independent Angela Christofilou/The Independent Put It To The People march: Best of The Independent’s pictures Put It To The People protest 23 March 2019 Angela Christofilou/The Independent Angela Christofilou/The Independent Put It To The People march: Best of The Independent’s pictures Put It To The People protest 23 March 2019 Angela Christofilou/The Independent Angela Christofilou/The Independent Put It To The People march: Best of The Independent’s pictures Put It To The People protest 23 March 2019 Angela Christofilou/The Independent Angela Christofilou/The Independent Put It To The People march: Best of The Independent’s pictures Put It To The People protest 23 March 2019 Angela Christofilou/The Independent Angela Christofilou/The Independent Put It To The People march: Best of The Independent’s pictures Put It To The People protest 23 March 2019 Angela Christofilou/The Independent Angela Christofilou/The Independent

The comments, to Sky News’ Sophy Ridge on Sunday programme, follow Ms May and Jeremy Corbyn uniting – in the wake of their joint local elections defeat – to push harder for a deal between the big two parties to secure Brexit.

The prime minister has conceded a form of customs union, but it falls short of Labour’s demands and for it to be locked into domestic legislation to prevent Boris Johnson, or another Brexiteer future prime minister, unravelling it.

Meanwhile, Mr Corbyn faces a huge backlash from around 100 of his MPs who insist no deal should be done without giving the public the Final Say in a fresh referendum.

Keir Starmer, the shadow Brexit secretary, has also sought to apply the brakes, saying on Saturday: “We’re still talking, that’s a good thing, but breaking the impasse can’t just be a case of bailing out the government.”

Rory Stewart, the new international development secretary, made clear the ball was in Labour’s court, after the prime minister almost begged him to ‘do a deal”.

“A lot of this rests on one man, whether Jeremy Corbyn really wants to deliver a Brexit deal,” he admitted.

Mr Stewart declined to say a deal “would” be done, saying “I think” it will, but claimed the two parties were only “a quarter of an inch apart”, adding: “We agree on 99 per cent of this.”

However, confusingly, he also attacked Labour’s demand for a decisive say over the EU’s trade negotiations as “something that doesn’t really exist out there in the real world”.

Earlier, the prime minister pleaded with Mr Corbyn to sign up, saying: “We will keep negotiating, with more formal talks due to take place on Tuesday, and keep trying to find a way through.