Cross-party talks between Theresa May and Jeremy Corbyn are to continue on Thursday after the Labour leader described the Brexit discussions as "useful but inconclusive".
Number 10 described Wednesday's talks as "constructive, with both sides showing flexibility and a commitment to bring the current Brexit uncertainty to a close.
"We have agreed a programme of work to ensure we deliver for the British people, protecting jobs and security."
Meanwhile the Labour leader said "there hasn't been as much change as I expected but we are continuing to have some discussions tomorrow morning to explore some of the technical issues".
Mr Corbyn added he put forward Labour's view that "we want to achieve a customs union with the European Union, we want to have access to the market and, in particular, we discussed the dynamic regulatory alignment that is guaranteeing European regulations as a minimum on the environment as well as consumer and employment rights".
Also on Wednesday in the Commons, MPs have voted to allow for extra time for a second reading on Yvette Cooper's European Union Withdrawal Bill and are now voting on amendments to it.
The Labour MP's bill would require Mrs May to ask European leaders for an extension to the Article 50 process beyond April 12 to avoid a no-deal Brexit.
However, Brexit minister Robin Walker warned that the Bill, in its current form, could actually increase the risk of an accidental no-deal Brexit.
ITV News' Europe Editor James Mates explains Europe's reaction to any short extension requests and EU's worries of a long extension
Which amendments to the bill have been voted on?
MPs voted against Tory ex-minister George Eustice's amendment 21 - which was part of his attempt to restrict the scope and power of the Bill - by 313 votes to 304, majority nine.
MPs defeated the Government's amendment 22, which aimed to prevent the Bill from limiting the powers of a minister to seek/agree an extension of the Brexit process - by 400 votes to 220, majority 180.
MPs voted down Tory Anne Main's amendment one, to prevent the PM from agreeing a delay to Brexit beyond May 22 - by 488 votes to 123 - majority 365.
Opening the debate on the legislation, Ms Cooper said her two-clause bill, which aims to avoid a no-deal Brexit, was "very simple".
"I think at the moment we all know there is no agreement and no consensus on the best way forward.
"We hope we can reach it, but at the moment there is no agreement," she said.
"Let's at least sustain our agreement about ruling out the worst way forward."
Ms Cooper added: "I know that there are members across this House and there are people across the country who say they would like to see no-deal happen and they would like to see it happen as soon as possible.
"I would just simply say, it will hit other people's lives and it's not fair."
It came after MPs delivered the first tie in a vote since 1993 over a proposal seeking to allow a third round of indicative votes on Brexit alternatives.
They voted by 310 to 310 on Labour MP Hilary Benn's amendment, with Speaker John Bercow casting his vote, in line with precedent, with the noes.
It came after Brexit minister Chris Heaton-Harris resigned from the Government, telling the Prime Minister he truly believes the UK "should have honoured the result of the 2016 referendum" and left the EU on March 29.
While Wales minister Nigel Adams also resigned on Wednesday, denouncing Mrs May's decision to meet Mr Corbyn as a "grave error".
The Selby and Ainsty MP - a close ally of Boris Johnson who took part in planning for his abortive push for the leadership in 2016 - told Mrs May in a letter: "It now seems that you and your Cabinet have decided that a deal cooked up with a Marxist who has never once in his political life put British interests first is better than no deal.
"I profoundly disagree with this approach."
Commenting on the cross-party talks during Prime Minister's Questions (PMQs), Tory MP Lee Rowley pointed out last week Mrs May had said "the biggest threat to our standing in the world, to our defence, and to our economy" was Mr Corbyn, asking: "In her judgement what now qualifies him for involvement in Brexit?"
The Prime Minister replied that "every member of this House is involved in Brexit", and said "the public want us to work across this House to find a solution that delivers on Brexit, delivers on the referendum, and gives people their faith the politicians have done what they asked and actually delivered for them".
As Mrs May and Mr Corbyn met for Brexit talks, leaders and spokespeople of other opposition groups agreed to make a People's Vote their priority.
In a joint statement, the SNP's Westminster leader Ian Blackford, Liberal Democrat leader Sir Vince Cable, Green MP Caroline Lucas, Plaid Cymru Westminster leader Liz Saville-Roberts and The Independent Group spokesperson Chuka Umunna said: "Given everything we now know - and the detrimental impact Brexit will have on the UK's economy, job opportunities and people's livelihoods, the priority must be bringing the issue back to the people in a People's Vote - with the option to remain on the ballot paper.
"Time is fast running out and any compromise that is reached must be brought back to the people through a fresh referendum, and keep the option to revoke Article 50 on the table to avoid a no-deal Brexit."
The meeting between Mrs May and Mr Corbyn was positively met by leaders on the Continent, with the European Parliament's Brexit co-ordinator Guy Verhofstadt said he hoped they could "give a solution".
Arguing against granting a long extension to the UK's EU membership due to fears gains made in negotiations could be undone, Mr Verhofstadt said: "We cannot risk giving the keys of the EU's future to a Boris Johnson, or a Michael Gove, the architects of this Brexit disaster.
"A long extension would do exactly that."
Irish premier Leo Varadkar has said he hopes Jeremy Corbyn will show leadership and come up with a compromised plan when discussing Brexit with Theresa May.
"I don't know if Mr Corbyn will rise to the occasion, whether he will show leadership and be able to come up with a compromised plan with Prime Minister May.
"I hope he does, but we will see if that happens in the next couple of days."
However, others were less positive, with European Commission President Jean-Claude Juncker saying that a no-deal Brexit is becoming "more and more likely".
Speaking in Brussels, he said: "The European Council has given all necessary time and space to the UK to take its decision.
"I believe a no-deal on the 12th April at midnight has become a scenario which looks more and more likely."
He added: "It's not what I want but we have made sure that the EU is ready to face up to that situation.
"We've been preparing since December 2017."
Mr Juncker also warned the UK would be more affected than the EU in the event Britain crashes out of the bloc, but "disturbances suffered by citizens (and) businesses in almost all sectors will be unavoidable".
Mrs May wrote to Tory MPs ahead of her meeting with Mr Corbyn, appealing for unity after causing anger among swathes of Brexit supporting Tories by proposing the talks with Labour.
She said: "I realise some of you will be concerned about the Government discussing the way forward with the Opposition.
"However, with some colleagues unwilling to support the Government in the division lobbies, this is the only way to deliver the smooth, orderly Brexit that we promised and for which the British people voted."
Watch PMQs in full: