A group of Labour MPs, Lords, and MEPs are urging Jeremy Corbyn to reject a hard Brexit deal and do more to defend the UK's membership of the single market.
At the same time, a group of some 30 Conservative MPs are lobbying Theresa May to rule out walking away from Brexit without a deal with the EU, as she goes into Wednesday's Queen's speech as the first prime minister in decades to announce a legislative programme without a House of Commons majority.
Leading centrist figures within the Labour party – including Stephen Doughty, Chuka Umunna, and 49 others – have signed a letter sent to The Guardian headlined: "As Labour politicians, we reject a hard-right Brexit, and defend the single market."
Shadow ministers Ruth Cadbury, Andy Slaughter, and Daniel Zeichner are among the signatories, as is opposition whip Thangam Debbonaire.
The letter says:
At the very least we should strongly oppose May’s decision to take [single market] membership off the table in these negotiations. An ambitious and confident alternative government – with Corbyn at the helm – should not throw in the towel as May has done, but could seek membership with reforms on immigration and the other matters we seek.
The MPs argue that a "motley crew of hard-right, pro-Brexit Tories" who passionately campaigned for Brexit, including Michael Gove and Boris Johnson, "want us to leave precisely because they want to roll back the social protections delivered by single market membership."
Corbyn has argued that the EU referendum result meant that the UK couldn't stay in the single market. Instead he has suggested the country should fight for "tariff-free access to the single market".
Shadow chancellor John McDonnell has also stopped short of defending single market membership.
.@johnmcdonnellMP clear -@UKLabour remain committed to leaving the EU single market #Peston
But the letter warns that ending the UK's membership of the single market would hinder Labour's ability to halt the spending cuts and public sector pay freezes of austerity.
The Guardian reports that some of the letter's signatories are forming an anti-hard-Brexit group within the parliamentary Labour party to oppose any Brexit deal that weakens the economic relationship between the UK and the continent.
Meanwhile, ahead of the Queen's speech to open the new session of parliament later on Wednesday, the Conservative party is facing a similar rebellion over Theresa May's assertion that "no deal is better than a bad deal" in the Brexit negotiations.
Sky News and others report that at least 30 Tory MPs have told party whips that they would not support any move to walk away from the negotiating table in Brussels with no agreement at all.
Chancellor Philip Hammond put himself at odds with the prime minister in his Mansion House speech on Tuesday when he said "no deal would be a very, very bad outcome".
The Conservative leadership is still locked in talks with Northern Ireland's DUP to provide a slim Commons majority, amid reports that negotiations have stalled.
Damian Green, the first secretary of state, told the Today programme on Wednesday morning that a deal was still possible.
"There’s still the possibility, there’s every possibility of a DUP deal," he said. "The talks have been taking place in a constructive way. Clearly, two political parties, we have some differences. But we have a lot in common."
The DUP warned the Tories not to take it for granted and said that "Conservative high command ought to stop their backbenchers whingeing about the DUP and show our party some respect."