Writing in two Sunday newspapers, May said she was "getting on with the job" despite facing criticism from both Remain and Leave camps within her own party over the second phrase of negociations.
The Brexit "war cabinet" - a sub-committee of senior ministers chaired by Mrs May - will meet on Monday to thrash out its stance on post-Brexit trade and an "implementation period".
The EU's negotiating guidelines make clear that the bloc expects the UK to observe all of its rules - including on freedom of movement - and accept the jurisdiction of the European Court of Justice (ECJ) during this time.
But backbench Tory Eurosceptics have said they will not accept arrangements which closely resemble continued EU membership during the transition to a new relationship.
Writing in the Sunday Telegraph, Mrs May said: "In the face of those who want to talk Britain down, we are securing the best and most ambitious Brexit deal for our whole United Kingdom.
"And my message today is very clear: we will not be derailed from this fundamental duty to deliver the democratic will of the British people."
Mrs May said: "Brexit allows us to seize the exciting opportunities outside the EU - with Britain in control of our borders, and setting our own laws - while building the new European economic and security relationship that I have proposed.
"So we will approach these discussions with ambition and creativity."
Boris Johnson called for the prime minister to strike a deal with Brussels that would allow the UK to ditch EU laws.
In a Sunday Times interview, the foreign secretary set out his vision for a UK-EU trade deal that would "maximise the benefits of Brexit" by allowing Britain the freedom to diverge from Brussels' laws.
He called for a deal that "gives us that important freedom to decide our own regulatory framework, our own laws and do things in a distinctive way".
Meanwhile, chancellor Philip Hammond faced a backlash from prominent Brexiteers for saying a transition deal would "replicate the status quo".
Former Brexit minister David Jones condemned the Chancellor, claiming he "appears only too ready to do Brussels' bidding" by signalling acceptance of the EU's position.
Ex-Tory leader Iain Duncan Smith accused Mr Hammond of "undermining" Mrs May, while prominent backbencher Jacob Rees-Mogg said the EU's position would reduce the UK to the status of a "colony".