The prime minister said the UK remained “firmly on course” to leave the EU with a deal “if MPs hold their nerve”.
A number of amendments to the government negotiating strategy will be voted on in the Commons on Wednesday.
The votes are not on Mrs May’s Brexit deal itself, but they will show what support she can or cannot get.
After her Brexit deal was overwhelmingly rejected by MPs last month, the prime minister has been trying to seek assurances from the EU to address MPs’ concerns.
She is still in talks with Brussels over the Irish backstop policy in her plan – which aims to prevent a hard border returning to the island of Ireland – and has assured MPs they will get to vote again on the deal by 12 March – just 17 days before the UK’s scheduled leaving date.
However, on Tuesday, Mrs May bowed to pressure to accept that the 29 March deadline might not be achievable, and promised MPs a vote on whether or not to delay Brexit or rule out leaving the EU without a deal if her plan is rejected for a second time.
In the Mail, Mrs May stressed that she did not want to see the Article 50 process extended and her “absolute focus” was on getting a deal in place for 29 March.
The prime minister’s critics have accused her of “kicking the can down the road”, but she insisted her efforts to persuade the EU to make concessions had “already begun to bear fruit”.
Environment Secretary, Michael Gove said that Mrs May had “done the right thing”, saying: “I think it’s important that we concentrate everyone’s mind on trying to make sure that we get a deal.”
Leader of the House of Commons Andrea Leadsom said that the government was “not talking about delaying Brexit”.
“The prime minister’s completely clear – she does not want to delay Brexit and nor do I,” she said.
Work and Pensions Secretary Amber Rudd denied any intentions to frustrate Brexit and said: “I’m part of a plot to back the prime minister and make sure we get a good Brexit deal through Parliament as soon as possible.”
Meanwhile, Jacob Rees-Mogg, the leader of the Eurosceptic European Research Group of Conservative MPs, told BBC Radio 4’s Today programme that he “can live with the defacto removal” of the backstop – which has been a sticking point for Mrs May’s deal in Parliament.
“I mean that if there is a clear date that says the backstop ends and that is in the text of the treaty or equivalent to the text of the treaty – if it was to be an appendix to the treaty…then that would have a reasonable effect from my point of view,” he said.
Critics dislike the backstop because they believe it kept the UK too closely aligned to the EU and fear that it could become permanent.
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