Labour is pressing the government to give MPs the chance to debate Theresa May's plans for the Irish border backstop before she flies to a crunch summit with European Union leaders this week. Many, notably French President Emmanuel Macron, made clear at a summit with May last month that they would agree to meet only if she could show she had come sufficiently close to a deal to make it worthwhile.
Mrs Foster said the PM should learn from Margaret Thatcher who "deeply regretted" being persuaded to sign the 1985 Anglo-Irish Agreement, which gave the Irish government a formal say in Northern Ireland affairs for the first time.
The issue of the border between Northern Ireland and Ireland is one of the last remaining obstacles to achieving a divorce deal with Brussels, with wrangling continuing over the nature of a "backstop" to keep the frontier open if a wider UK-EU trade arrangement can not resolve it.
A spokesman said: "In the last few days United Kingdom and European Union negotiators have made real progress in a number of key areas".
One of the issues that has been hampering progression of a deal has been that of the Irish border and a potential backstop - a mechanism to avoid a hard border with Northern Ireland.
The warnings came in the latest no-deal Brexit technical notices released by the Government, of which 29 papers were published in total.
But with Mrs May under increasing pressure from Tory Eurosceptics and her DUP parliamentary allies, the Government also has a reason to appear to be taking a tough line.
Both sides want to avoid renewed checks on what will become their only land border to avoid hindering trade on the island of Ireland and reawakening tensions two decades after a peace deal ended 30 years of violence in Northern Ireland.More news: Merkel's Bavarian Allies Lose Absolute Majority in Regional Vote
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In a strongly-worded article in the Belfast Telegraph, Mrs Foster warned against the EU's backstop proposal and also stressed that she would not accept any measure that resulted in extra checks for goods travelling between Great Britain and Northern Ireland.
However, Brexiteers like Patel and Davis suspect this could turn into a permanent situation, restricting Britain's freedom to strike future trade deals with other countries.
Former Brexit secretary David Davis yesterday launched his own call-to-arms to members of the Cabinet to exert their "collective authority" and reject Theresa May's proposed Brexit deal.
It follows reports that several Eurosceptic Cabinet ministers will hold a meeting this evening to coordinate their response to Mrs May's Brexit plans. Penny Mordaunt, the global development secretary, and Esther McVey, the work and pensions secretary, and Andrea Leadsom have the most significant concerns over the plans, although they did not attend last night's meeting.
But she added: "Getting May out and him becoming an interim leader may be the only way to deliver Brexit and FTA (a free-trade agreement)".
Ms Dorries said that Mr Davis had always focused on changing the policy, rather than the Prime Minister.
But senior Labour sources suggest that if May lost the meaningful vote, the party would first press for her to return to Brussels and shift her negotiating stance towards a deal including a customs union, that could then win the backing of parliament.
But shadow foreign secretary Emily Thornberry told the BBC: "If she comes back with something that's just a fudge she's cooked up with Brussels... we're not voting for something that's essentially a bridge to nowhere".