Leading Conservative eurosceptics increased pressure on embattled British Prime Minister Theresa May yesterday by issuing a joint ultimatum with Northern Ireland's Democratic Unionist Party (DUP), demanding she change her Brexit plan. Steve Baker, deputy chair of a group of some 80 eurosceptic lawmakers from May's Conservatives, warned that his group will vote against May's plan in Parliament if she refuses to change it.

The eurosceptics want May to drop her acceptance of a backstop that guarantees an open Irish border but could leave Northern Ireland under different customs arrangements from the rest of the United Kingdom.

"We share the prime minister's ambition for an EU free trade agreement, but not at any price and certainly not at the price of our union," Baker wrote in a joint article with DUP Brexit spokesman Sammy Wilson for the pro-Conservative Sunday Telegraph. "If the government makes the historic mistake of prioritizing placating the EU over establishing an independent and whole U.K., then, regrettably, we must vote against the deal," they said.

Their threat comes amid pressure on May from both pro-EU and pro-Brexit Conservatives, and speculation that more ministers could resign.

May was shaken late Friday when a junior minister resigned with a powerful attack on her Brexit negotiations and a call for a second referendum on leaving the EU. Jo Johnson said May was offering Britain a "false choice between [her Brexit] deal and ‘no deal' chaos." Her plans were a "travesty of Brexit" and would produce "no real clarity about how this situation will ever end," Johnson said.

May is also facing mounting pressure on the Irish border question. Britain cannot push for a unilateral mechanism to end a so-called backstop arrangement to prevent the return of a hard border between Northern Ireland and EU-member Ireland, Education Minister Damian Hinds said yesterday. His words will further anger eurosceptics in Prime Minister May's Conservative Party who fear the backstop, an insurance policy if a deal on future ties does not guarantee an open border, could keep Britain in the European Union's customs union indefinitely.

"The prime minister has to negotiate something which is negotiable with the other side as well as working for people here. If we have too hard a line about saying that we must have a totally unilateral exit or there's an absolutely fixed, hard end date, it is very, very unlikely that that is going to be negotiable with the other side," Hinds told the BBC's Andrew Marr Show.

"But on the other hand, people here rightly want comfort... and confidence that it isn't an open-ended thing, so there must be some sort of way of giving that comfort and confidence to people; but exactly what the shape of that is, that is at the heart of these discussions," he added.

Regardless, 10 Downing Street insisted that the government would not strike an agreement "at any cost" to reach EU demands.