THERESA May has warned that a second referendum on Brexit could damage the country’s “social cohesion” and would strengthen the hand of Scottish Nationalists, who want to “break up our United Kingdom” in another independence vote.

Updating MPs on what she saw as the next steps in the Brexit process, the Prime Minister did not present a new detailed plan but made clear, after more talks with colleagues and others, Plan B would centre on changing the Irish backstop 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”.

She added: “I will then take the conclusions of those discussions back to the EU." This is expected to be a precursor to a second “meaningful vote” of MPs on a rejigged proposal some time in February.

Mrs May told MPs she did not think there was a majority at Westminster for a second EU referendum, warning: "There has not yet been enough recognition of the way a second referendum could damage social cohesion by undermining faith in our democracy."

Later, her spokesman, questioned if she was alluding to potential violence on the streets, said she was merely expressing concern 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.

The PM also said: “I fear a second referendum would set a difficult precedent that could have significant implications for how we handle referendums in this country; not least, strengthening the hand of those who are campaigning to break up our United Kingdom.”

But Scottish Labour’s Ian Murray, who supports a People’s Vote, accused Mrs May of “utter hypocrisy,” claiming she was determined to press ahead with a “reckless Brexit that puts the future of the UK at risk”.

In a move welcomed across the Commons chamber, the PM announced the scrapping of the £65 administration fee for EU nationals wanting to remain in the UK after Brexit.

She promised to guarantee workers' rights and environmental safeguards and said she would continue talks to find "the broadest possible consensus" on the way forward.

Earlier in the day, David Lidington, her de facto deputy, held cross-party talks with Remainer MPs, including Labour’s Chuka Umunna and Chris Leslie, who defied Jeremy Corbyn’s instruction not to attend.

The Labour leader again denounced the talks as a “PR sham,” exhorting Mrs May to “change her red lines because her current deal is undeliverable".

Ian Blackford for the SNP claimed she was not interested in meaningful talks but declared: “We have an escape route from the chaos of Brexit: an independent Scotland.”

The PM hit back, saying the Nationalists’ claim that the best economic future for Scotland was to be outside the United Kingdom was to “fly in the face of economic reality”.

She announced a meeting with Nicola Sturgeon later this week to talk about the Scottish Government’s “enhanced role” in the future trade talks with the EU.

But the First Minister tweeted: "Fair to say we've had empty and undelivered promises like this for two and half years now. Will be interested to hear what's going to be different now but experience tells me to be very sceptical."

Next week, MPs will debate Brexit ahead of a range of non-legally binding indicative votes on various options. The first in a series of amendments began to be tabled on Monday night.

Labour tabled one calling on the Government to rule out a no-deal Brexit and allow MPs to vote on other options, including its own plan for a customs union with the EU and a strong single market relationship.

Mr Corbyn said MPs must now “break the deadlock,” adding: “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."

A cross-party group of MPs, led by Labour’s Yvette Cooper, published a bill, which would allow Mrs May until February 26 to secure a new deal before the Article 50 process would be extended nine months to prevent Britain crashing out without a deal.

In other developments:

*Jacek Czaputowicz, Poland’s Foreign Minister, broke ranks with the EU27, suggesting a five-year time-limit to the Irish backstop;

*it emerged Amber Rudd, the Work and Pensions Secretary, warned Downing St it could face up to 40 ministerial resignations next week if Tory MPs were prevented from voting to stop a no-deal outcome;

*Simon Coveney, Ireland’s Foreign Minister, said, following talks in Brussels, that Michel Barnier, the EU’s chief Brexit negotiator, had assured him the EU27 remained "firmly supportive" of the Withdrawal Agreement in full, including its guarantees of no hard border in Ireland;

*Emily Thornberry, the Shadow Foreign Secretary, suggested Labour might not back a second referendum unless the UK were "about to hit the wall of no-deal";

*Richard Harrington, the Business Minister, warned crashing out of the EU without a deal would be an "absolute disaster" as he urged the PM to rule out a no-deal Brexit;

*The UK Governments and its Spanish counterpart signed an agreement to safeguard voting rights in local elections for their citizens residing in the other country regardless of the way Brexit unfolds and

*Jacob Rees-Mogg, the ardent Brexiteer, said he would be open to the idea of Nigel Farage, the former Ukip leader, joining the Conservative Party in the future but noted: “Perhaps a little bit more purdah is required."