Theresa May has warned that a second EU referendum could “damage social cohesion”, as she set out plans to find a Brexit deal which could win parliamentary support.

The Prime Minister said she would conduct further talks on the controversial Brexit backstop, and promised to give Parliament “a proper say” in negotiations on the future relationship between the UK and EU.

But she refused to rule out a no-deal Brexit, and insisted that there was no majority in the House of Commons for a so-called People’s Vote.

In a statement to the Commons, Mrs May acknowledged that last week’s emphatic rejection of her Withdrawal Agreement by MPs meant that the Government’s approach to Brexit had to change. And she insisted that it had.

She announced she was scrapping a £65 fee for EU nationals wanting to remain in the UK after Brexit, promised to guarantee workers’ rights and environmental safeguards and said she would continue talks to find “the broadest possible consensus” on the way forward.

Labour put down an amendment to the Government’s Brexit motion which party leader Jeremy Corbyn said was aimed at preventing a no-deal withdrawal from the EU.

The Labour amendment states that options to prevent a no-deal exit should include negotiating changes to “secure a permanent customs union with the EU” and “legislating to hold a public vote on a deal or a proposition that has commanded the support of the majority of the House of Commons”.

Mr Corbyn said: “Our amendment will allow MPs to vote on options to end this Brexit deadlock and prevent the chaos of a no deal.

“It is time for Labour’s alternative plan to take centre stage, while keeping all options on the table, including the option of a public vote.”

Mrs May said that the Government had conducted cross-party talks since her Commons defeat in a “constructive spirit”, and regretted Jeremy Corbyn’s decision to boycott them.

But Mr Corbyn dismissed the talks as “a PR sham”, telling MPs: “The Prime Minister must change her red lines, because her current deal is undeliverable.”

And the Labour chairman of the Commons Exiting the EU Committee, Hilary Benn – who has been pushing for a series of indicative votes on Brexit options, said: “I am sorry to say while her door may have been open, her mind has remained closed.”

Mrs May set her face firmly against a People’s Vote, warning MPs: “There has not yet been enough recognition of the way that a Second Referendum could damage social cohesion by undermining faith in our democracy.”

She said she did not believe there was a majority in the Commons for a fresh poll, and insisted it was the “duty” of MPs to deliver on the result of the 2016 vote.

And she said that a no-deal outcome could be secured only by revoking the UK’s declaration of its intention to quit the EU under Article 50 of its treaties, something she was not prepared to do.

Brexit
Mrs May addressed MPs six days after their overwhelming rejection of her Brexit plans (House of Commons/PA)

Aides later said that Mrs May was concerned over the possibility of “bad feeling or rancour” and harm to trust in democracy if the majority who voted Leave in 2016 felt their voice was being ignored.

Mrs May made no specific proposals on the backstop, which is designed to ensure an open border in Ireland after Brexit, but has raised concerns about the possibility of the UK being trapped in a customs union with the EU for an indefinite period.

She told MPs: “I will be talking further this week to colleagues – including in the DUP – to consider how we might meet our obligations to the people of Northern Ireland and Ireland in a way that can command the greatest possible support in the House.

“And I will then take the conclusions of those discussions back to the EU.”

Irish foreign minister Simon Coveney held talks with EU chief Brexit negotiator Michel Barnier in Brussels (European Commission Audiovisual Services/PA)

Mrs May’s statement came as Poland broke ranks with the rest of the European Union by suggesting that the Brexit deadlock could be ended by putting a five-year time limit on the backstop.

Following talks in Brussels, Irish foreign minister Simon Coveney said Brexit negotiator Michel Barnier had assured him the EU remains “firmly supportive” of the Withdrawal Agreement in full, including its guarantees of no hard border in Ireland.

While the EU was prepared to be “flexible” on the Political Declaration on future relations, it was not willing to renegotiate the Withdrawal Agreement to secure a deal, said Mr Coveney.

Mr Barnier himself said: “We are working 27 as a team, a single team and we negotiate as one.”

Poland’s foreign minister Jacek Czaputowicz signalled a different approach from Warsaw, telling the Rzeczpospolita newspaper: “If Ireland asked the EU to amend the agreement with the British on the backstop so that it would apply temporarily – let’s say five years – the matter would be solved.

“It would obviously be less favourable for Ireland than an indefinite backstop, but much more advantageous than no-deal Brexit.”

Mr Czaputowicz said that London and Dublin were “playing chicken” over the border and risked a “head-on collision” in which Ireland stood to “lose the most”.

But Mr Coveney said: “Putting a time limit on an insurance mechanism – which is what the backstop is – effectively means it is not a backstop at all.”

And Germany’s foreign minister Heiko Maas played down the Polish initiative, telling reporters: “I am completely with my Irish colleague. He has already said what he thinks of it, which is nothing.”

Mrs May sought to reassure MPs that they will be given “a proper say and fuller involvement” in establishing the UK’s position in negotiations on future relations with the EU.

The Government will consult the Commons on its negotiating mandate and will regularly update the House during talks, she promised.

And she said that the Government would offer private and confidential briefings to backbench select committees to ensure MPs are kept up-to-date on the progress of talks without undermining the UK’s position.

Border graphics
(PA Graphics)

A senior member of Angela Merkel’s Government, industry minister Peter Altmaier, warned against trying the EU’s patience for political reasons.

“Sympathy, patience and readiness to wait until the UK’s position will be clarified are of utmost important to avoid the worst,” warned Mr Altmaier.

“They should not be misused for party politics. Large majority wants to exclude hard Brexit – in the interest of the UK and beyond.”

Unusually, MPs are able to amend the so-called “neutral motion” tabled by the Prime Minister, with votes due to take place on January 29.

One group, including senior Labour MP Yvette Cooper and Tory former minister Nick Boles, is seeking to give time for a Bill to suspend the Article 50 withdrawal process if there is no new deal with Brussels by the end of February.

Another more radical amendment drawn up by former attorney general Dominic Grieve would allow a motion by a minority of 300 MPs – from at least five parties and including 10 Tories – to be debated as the first item of Commons business the next day.