The Prime Minister said she found “real determination” in Brussels to find a way through the deadlock on negotiating a deal, and claimed engagement with the EU had “already begun to bear fruit”.
Mrs May accepted for the first time on Tuesday that the UK may not leave the EU on March 29, offering MPs a chance to vote to delay Brexit if her deal is rejected again next month.
She said Parliament’s “absolute focus should be on working to get a deal and leaving on March 29” – and reiterated her opposition to delaying Britain’s departure.
Writing in the Daily Mail, Mrs May said: “By committing Labour to holding a second referendum, despite promising to implement Brexit, Jeremy Corbyn has shown once again that he cannot be trusted to keep his promises. His cynical political games would take us back to square one.
“Instead, Parliament should do its duty so that our country can move forward. We want to leave the EU with a deal that gives us the best of both worlds: a close relationship with our nearest neighbours and the chance to make the most of our talents and resources by building new relationships with growing economies around the world.”
MPs will vote on the Prime Minister’s negotiating strategy for Brexit and a series of amendments on Wednesday evening, ahead of another “meaningful vote” on her Withdrawal Agreement next month.
Mrs May was warned by a ministerial aide that she faces an “enormous defeat” in the Commons on Wednesday unless she gives in to demands to seek a treaty on citizens’ rights after Brexit.
More than 60 Conservatives are understood to have signed an amendment tabled by Alberto Costa calling for a separate agreement with the European Union to protect the rights of expats even if there is a no-deal Brexit.
Labour is also supporting the amendment and Mr Costa said it would be a “farce” if the Government did not back down.
Mr Costa said his amendment, which already has support from 130 MPs ranging from Labour leader Mr Corbyn to Tory arch-Eurosceptic Jacob Rees-Mogg, would give the Prime Minister a mandate to push for a change with her fellow EU leaders.
He said his own job as a parliamentary private secretary (PPS) to Scottish Secretary David Mundell was on the line as a result of his actions.
Labour former minister Yvette Cooper will table an amendment seeking to pin the Prime Minister down to her commitment to give MPs a chance to vote to delay Brexit if her deal falls again.