Jeremy Corbyn and Theresa May discussed the ‘soft Brexit’ option of staying in a customs union when they finally met for face-to-face talks in the Commons, Labour has revealed.

In a stark contrast to the two leaders’ sparky exchanges during Prime Minister’s Question Time, the pair held a “serious and engaged” private meeting in May’s office to find a way forward on UK-EU relations.

Corbyn, who had refused to meet the PM until the prospect of a no-deal Brexit was off the table, spent 45 minutes with her along with shadow chief whip Nick Brown, his chief of staff Karie Murphy and strategy director Seumas Milne.

In a glimmer of hope of a cross-party agreement, Corbyn’s spokesman said: “There was a detailed exchange of views on a customs union and a single market.”

Asked if May showed any softening of her views, he replied “she was interested in exploring the detail”.

But the Labour leader also said later that he was ‘suspicious there’s a programme of running down the clock’ to exiting without at deal on March 29.

The Conservative party refused to comment on the content of the meeting.

May has repeatedly claimed that a customs union would undermine the UK’s ability to strike independent trade deals with non-EU countries, although some ministers believe the idea is worth exploring.

But Labour has pushed the idea, as well as a ‘strong single market’, as its own alternative to May’s Brexit plans, claiming it would retain frictionless trade with Europe that many businesses want.

Corbyn and May agreed to meet again in coming days, although there was no timetable for exactly when the next encounter would take place.

After the meeting, Corbyn said: “I asked for the Prime Minister’s assurance that we were not back into the territory of threatening no-deal as a way of getting support for her failed deal, which has obviously got very limited support in parliament.”

The Labour leader also revealed that he was willing to look again at a fresh Commons amendment to bind May’s hands to delay Brexit if the UK looked like it was set to crash out of the EU without an agreement.

He said he was “extremely disappointed” with the 14 Labour MPs who voted against Yvette Cooper’s move this week to force the PM into ruling out a no-deal exit.

“I’m very disappointed of those that chose to vote with the Conservatives last night on those issues,” he said.

Corbyn added that he will be having ‘discussions’ with the five frontbenchers who abstained on the proposal.

MPs voted by a narrow majority of eight votes for a separate, non-binding amendment by Tory Caroline Spelman and Labour’s Jack Dromey, that ruled out a no-deal exit from the EU.

Many Labour MPs and members fear a hard Brexit after the PM caved to pressure from her Tory Eurosceptics on Tuesday to reopen her deal with Brussels.

EU leaders made clear on Wednesday that they would not renegotiate the ‘withdrawal agreement’ that had been hammered out between UK and the 27-nation bloc over the past two years.

Senior MEP Philippe Lamberts, part of the European Parliament’s Brexit steering group, warned that protecting EU trade was the priority. “If we have a choice to make between two evils, well then no deal is the lesser evil,” he said.

Earlier, at PMQs, the pair clashed as usual over Brexit. Corbyn said the prime minister may have succeeded in “temporarily uniting her very divided party” in Tuesday’s votes on amendments to her plan but she had to make “more important compromises” to “unite the country”.

May said Corbyn was a “fine one to talk about coming together”, when he had only now agreed to meet her.

Pressed by the Labour leader on whether she would abide by the Commons vote on no-deal, May replied: “The House did vote to reject no deal, but that cannot be the end of the story.”

Later, a No.10 spokesman was asked if the PM viewed the Spelman-Dromey amendment vote as ‘morally binding’.

He replied: “Like all amendments, it’s an expression of the will of the House. All the PM is pointing out that factually the only way to give effect to that amendment is to agree a deal or to revoke Article 50, which we are not prepared to do.”