Commenting on reports that Mr Corbyn has changed his position on staying in the Customs Union, Birkenhead MP Frank Field said: "This is not what people voted for and it is playing with fire".
"Certainly, regardless of the nuanced legal opinion on protocols versus withdrawal agreements, what has happened is a political fudge".
The statement, signed by 37 MPs and a dozen peers, says: "Given the parliamentary arithmetic and the numbers of parliamentarians from other parties - including Conservative backbenchers - who have indicated they will join us in this endeavour, our country's continued participation in a customs union and the single market is now in the Labour party's hands".
She told ITV this would mean "we don't have to have a hard border between Northern Ireland and the Republic of Ireland" but - if the United Kingdom followed a Turkey-style customs agreement with the EU - Britain would still be able to "negotiate free trade agreements in relation to many other different areas".
EU President Donald Tusk dismissed the reported plans as "based on pure illusion".
"Whether it's our amendments or the cross-bench amendments, crunch time is now coming for the prime minister because the majority of Parliament does not back her approach to a customs union", Labour's Brexit spokesman, Keir Starmer, told BBC TV on Sunday.
May has ruled out any form of customs union with the EU after Brexit, saying that would curtail Britain's ability to broker new trade deals.
Labour's Brexit-backing MPs have repeatedly warned that shackling Britain to the European Union will lose the party's huge numbers of voters across the North of England.
It would involve reaching "a new treaty" because membership in the EU Customs Union would end when Britain is no longer an EU member, he said. "Yes, that's the intention".
Sir Keir said Labour had conducted "many weeks of discussion unanimously" and had agreed to develop their policy.
Tory Remainer Anna Soubry has tabled a cross-party amendment to the Trade Bill in an attempt to compel the Government to retain a customs union with the EU after leaving the bloc.
Mr Corbyn faces divisions within his own party with 80 senior figures from the party urging him to go further than committing to the customs union in his speech on Monday.
"So I concluded the meeting by reminding the committee that the decisions we make now will shape this country for a generation".
Ms Hoey, a former Labour minister, told the Telegraph: "I hope Jeremy will remember that in the last election our manifesto commitments on the EU helped ensure that many ex-Labour voters who had gone to UKIP came back to us on the understanding that he was committed to leaving the EU and not leaving in name only, which is what any form of customs union with the EU would mean".