The prime minister has said the government is “proving the doubters wrong” with its Brexit negotiations.
On Friday, EU leaders agreed talks on the implementation period and future trade could begin the new year.
Writing in two Sunday papers, Theresa May vowed she would “not be derailed” from securing an “ambitious” deal.
Meanwhile, Foreign Secretary Boris Johnson has warned the UK cannot mirror EU law in the long term or it would risk becoming a “vassal state”.
Cabinet ministers are due to discuss their stance on the relationship they want with the EU – the UK’s “end state” – in the coming days, but some ministers are thought to favour a closer alignment than that suggested by Mr Johnson.
However, writing in the Sunday Telegraph and Sunday Express Mrs May said: “Amid all the noise, we are getting on with the job.”
She said the last 10 days had “marked a watershed” in the Brexit process and that the government would now “begin to build that new, deep and special partnership” with the EU.
“This is the exciting part of the negotiations and there is no limit on our ambition and creativity,” she added.
BBC political correspondent Chris Mason said Mrs May had struck a defiant tone in her newspaper columns but that her challenge in 2018 would be to keep her party, and the country, on side as the negotiations continued.
Brexiteer Mr Johnson’s comments in a Sunday Times interview echoed those of his fellow Conservative MP Jacob Rees Mogg, who said on Friday the arrangements the EU had proposed for the transition period would make the UK “a vassal” – or subordinate – state of the EU.
The EU’s guidelines for phase two of the negotiations say the UK would “continue to participate in the customs union and the single market during the transition” and remain under the jurisdiction of the European Court of Justice.
Mr Johnson said if the UK ended up being forced to mirror EU laws “we would have gone from being a member state to a vassal state”.
He said Mrs May had done “a fantastic job moving us forward in the negotiations” before setting out what he believed the government should seek to get in its future trade deal with the EU.
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”, he said.
Meanwhile, two Tory peers have warned Mrs May she could face defeats in the House of Lords if the government tried to “bully” its members.
The prime minister suffered her first Commons Brexit defeat earlier this week when MPs -including 11 from her own party – voted to give Parliament a legal guarantee of a vote on the final Brexit deal struck with Brussels.
Following the vote there were calls for the Tory rebels to be deselected by the party and some received death threats.
Tory peers, Baroness Altmann and Baroness Wheatcroft, have written 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 added.