Many Conservative eurosceptics had made clear they would only consider supporting May's deal if she gave a firm commitment to resign, hoping a new leader would be more sympathetic to their views when negotiating the terms of Britain's future relationship with the EU.

"I have heard very clearly the mood of the parliamentary party," May told a meeting of Conservative lawmakers (MPs).

"I know there is a desire for a new approach – and new leadership – in the second phase of the Brexit negotiations – and I won't stand in the way of that."

But within hours of May's offer, the Democratic Unionist Party, which props up her minority government, said it would vote against the deal if May brought it back a third time.

"We're in a situation where we cannot sign up to the Withdrawal Agreement," DUP leader Arlene Foster said.

The government gave itself the option of bringing May's deal back to parliament on Friday, although speaker John Bercow repeated his warning that he would not allow a third vote unless the motion had changed substantially since its last defeat.

May, who voted to remain in the EU in the 2016 referendum, had already promised to step down before the next election, due in 2022.

Her deal, defeated in parliament by 149 votes on March 12 and by 230 votes on Jan 15, means Britain would leave the EU single market and customs union as well as EU political bodies.

But it requires some EU rules to apply unless ways can be found in the future to ensure no border posts need to be rebuilt between British-ruled Northern Ireland and EU member Ireland.

Many Conservative rebels and the DUP object to this "Irish backstop", saying it risks binding Britain to the EU for years.

To succeed, May needs at least 75 lawmakers to come over to her side.

After the ERG met, a spokesman said: "There is no way enough votes are coming out of that room to put the (Withdrawal Agreement) through."