Jeremy Corbyn will meet the EU’s Michel Barnier later in the wake of his offer to back Theresa May if she keeps the UK in a customs union.
The Labour leader dismissed the PM’s Chequers plan but said he could support a “sensible” deal on Northern Ireland, jobs and work rights.
MP Barry Gardiner told ITV’s Peston the offer was genuine and the party would “bend its red lines” if the PM did too.
But Health Secretary Matt Hancock said Labour could not be trusted on Brexit.
And Home Secretary Sajid Javid said talk of a referendum on the outcome of the Brexit negotiations – which Labour has said must remain an option – was “deeply unhelpful” to getting the best deal for Britain.
But illustrating divisions within the Conservatives, his predecessor Amber Rudd told ITV’s Peston that a new public vote was “absolutely” preferable to the UK leaving the EU next March without an agreement.
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And backbencher Nadine Dorries said Mrs May should step down as she had become “handcuffed” to the Chequers deal and was not communicating the benefits of Brexit.
The Labour leader last met Mr Barnier, who is conducting the negotiations on behalf of the other 27 EU members, in July 2017.
EU officials said the timing of Thursday’s meeting, coming just days before the start of the Conservative Party, was a coincidence and stressed that it was not part of the negotiations.
The meeting coincides with Mr Corbyn’s trip to the Belgian capital to witness a square being renamed in honour of Jo Cox, the Labour MP who was killed during the Brexit referendum.
The prime minister is under mounting pressure to rethink her approach after European leaders warned key parts of her Chequers blueprint, which would keep the UK closely aligned with the EU in trade in goods, for future relations with the EU were not viable.
Up to 40 Tory Brexiteers have said they will oppose her plan if it comes to a vote in Parliament.
In his keynote leader’s speech in Liverpool, Mr Corbyn said Labour would also vote against any deal based on Chequers, as it would be extremely unlikely to meet the party’s six tests.
But he said if the PM brought home a deal that “includes a customs union and no hard border in Ireland”, that protects jobs, people’s rights at work and environmental and consumer standards, it would get his backing.
Shadow international trade secretary Barry Gardiner said the offer was not a ruse and Labour was willing to compromise and “bend our own red lines in order to get a deal” if specific conditions were met.
Mrs May has rejected staying in any form of customs union, saying it will prevent the UK from signing trade deals with other countries and setting its own tariffs.
The BBC’s Brussels reporter Adam Fleming said Labour had clarified its position on Brexit and this was a chance for Jeremy Corbyn to explain it to the EU’s chief negotiator.
The opposition’s offer to stay in a customs union and to maintain high standards is much closer to the EU’s preferred outcome than the prime minister’s proposals, he added.
Diplomats from the EU’s 27 other members were briefed about the bloc’s planning for a no-deal Brexit on Wednesday after a leaked document said the work had to intensify because of uncertainty about whether a final deal can be reached and approved by the UK and EU Parliaments.