Writing in UK newspapers today, May said she is determined to get the most "ambitious" deal for Britain as it prepares to leave the 28-member economic bloc by March 2019.
"This is a government that is getting on with the job. We are proving the doubters wrong and we will stick to the task: securing the best possible Brexit and building a Britain fit for the future," she writes in 'The Sunday Telegraph'.
She said the talks with the EU would now move to the "exciting part" of discussions on the implementation period for Brexit and the future of trading relationships.
Despite her House of Commons defeat earlier in the week as a result of her own party's rebellion to vote with the Opposition on giving UK Parliament more say in the final Brexit agreement, May struck a defiant tone in her message.
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She spelt out her stance ahead of a crunch week for the UK government as the Cabinet prepares to discuss for the first time what the terms of a future deal with the EU should be.
UK Cabinet ministers are due to discuss the UK's "end state" plans as theBrexit "war cabinet" a sub-committee of senior ministers chaired by Theresa May will meet on Monday, with a meeting of the full Cabinet scheduled for Tuesday.
He believes the UK needs "something new and ambitious, which allows zero tariffs and frictionless trade" but maintains the freedom to "decide our own regulatory framework and own laws".
Many of his other Cabinet colleagues are in favour of a less hardline shift.
Meanwhile, two Conservative party peers have warned the British PM that she could face defeats in the House of Lords if the government tried to "bully" its members over the issue.
Following the vote there were calls for the Tory rebels to be deselected by the party and some reportedly even received death threats.
Baroness Altmann and Baroness Wheatcroft write in the 'Observer' that such threats "are worrying symptoms of the toxic atmosphere which has been created in our country".
"Mindful of the monumental importance for future generations of getting Brexit right, the Lords is unlikely to be receptive to bullying over a restricted timetable or vigorous whipping to toe the party line,"they warn.
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