Brexit secretary Stephen Barclay has held talks with advocates of a second referendum, as they laid out their proposals should a “new direction” be needed in the coming days.

In a sign that Downing Street is taking the prospect of a fresh vote seriously, the Labour MP Peter Kyle said Mr Barclay was “engaging fully” with possibilities, but had remained “loyal” to government policy to oppose a second referendum at all costs.

Alongside his colleague Phil Wilson, Mr Kyle has outlined a plan to help the prime minister’s Brexit deal get through the Commons on the condition of it then being put to the country in a second referendum.

A government source confirmed the 45-minute meeting went ahead when asked by The Independent, but insisted Mr Barclay regularly meets with MPs from all political parties.

The discussions come as Westminster prepares for yet another week of political turmoil with MPs gearing up to vote on the prime minister’s Brexit deal.

On Friday, Ms May herself admitted: “Reject it and no one knows what will happen. We may not leave the EU for many months, we may leave without the protections that the deal provides. We may never leave at all.”

Britain Before Brexit: Northern Ireland Show all 12 1 /12 Britain Before Brexit: Northern Ireland Britain Before Brexit: Northern Ireland Derry, Londonderry A garage door displaying unionism, bolted shut, like a visual representation of Brexit Britain, locked to outsiders, safeguarding what’s inside Richard Morgan/The Independent Britain Before Brexit: Northern Ireland Derry, Londonderry Rossville Street, the site of Bloody Sunday, where messages demand a severance with England. From this perspective, Britain is England in sheep’s clothing, the real empire, the centre of colonial power Richard Morgan/The Independent Britain Before Brexit: Northern Ireland Bangor A political message in paint not yet dry, still forming, setting, adjusting, or in old paint finally eroding, melting away Richard Morgan/The Independent Britain Before Brexit: Northern Ireland Bangor Moral judgement frames a residential view. The message seeks to make everybody involved in the religious narrative: those who don’t believe are those most in debt Richard Morgan/The Independent Britain Before Brexit: Northern Ireland Castlerock The beach is sparse and almost empty, but covered in footprints. The shower is designed to wash off sand, and a mysterious border cuts a divide through the same sand Richard Morgan/The Independent Britain Before Brexit: Northern Ireland Belfast Two attempts to affect and care for the body. One stimulated by vanity and social norms and narratives of beauty, the other by a need to keep warm in the winter night Richard Morgan/The Independent Britain Before Brexit: Northern Ireland Belfast The gate to an unclaimed piece of land, where nothing is being built, where no project is in the making, where a sign demands the creation of something new Richard Morgan/The Independent Britain Before Brexit: Northern Ireland Derry, Londonderry Under a motorway bridge a woman’s face stares, auburn and red-lipped, her skin tattooed with support for the IRA and a message of hostility to advocates of the Social Investment Fund Richard Morgan/The Independent Britain Before Brexit: Northern Ireland Derry, Londonderry The Fountain Murals, where the curbs and the lampposts are painted the red, white, and blue of the Union Flag. A boy walks past in the same colours, fitting the scene, camouflaged Richard Morgan/The Independent Britain Before Brexit: Northern Ireland Coleraine A public slandering by the football fields, for all to see or ignore. I wonder if it’s for the police or for the community Richard Morgan/The Independent Britain Before Brexit: Northern Ireland Belfast A tattoo parlour, where the artist has downed tools, momentarily, bringing poise to the scene, which looks like a place of mourning, not a site of creation Richard Morgan/The Independent Britain Before Brexit: Northern Ireland Derry, Londonderry A barrier of grey protects the contents of this shop, guarding it from the streets outside, but it cannot conceal it completely, and the colours of lust and desire and temptation cut through Richard Morgan/The Independent

Details of the meeting emerged as the shadow Brexit secretary Sir Keir Starmer said on Sunday that he expected there would be an opportunity for MPs to vote on a fresh referendum in the days ahead – either through a Labour amendment, or one tabled by backbenchers.

But Sir Keir made clear this will not happen on Tuesday when MPs vote on the prime minister’s withdrawal agreement for a second time. “I think there is a growing feeling that this Tuesday should be a straight up-and-down vote on the deal,” he told Sky News’s Sophy Ridge on Sunday programme.

Sir Keir continued: “I don’t know whether something dramatic will happen in the next 24 hours but unless it does, exactly the same deal is going to be put before parliament.”

“It doesn’t mean that a public vote is gone,” he added. “It doesn’t mean we won’t come to it. We will have to work with others. There is going to be plenty of opportunities for amendments.”

Mr Kyle, who revealed the meeting, told The Observer: “Clearly the Brexit secretary is fully engaged in the battle to deliver support for the vote on Tuesday.