May was applauded by European Union leaders in Brussels on Friday after securing an agreement to move previously-deadlocked talks forward onto the topic of interim and long-term trading arrangements.
The progress has gone some way to easing concerns of businesses and investors who fear Britain could crash out of the bloc without an exit deal, or that May's fragile government could collapse under the pressure of delivering Brexit.
"Amid all the noise, we are getting on with the job," May wrote in the Sunday Telegraph. "My message today is very clear: we will not be derailed from this fundamental duty to deliver the democratic will of the British people."
But May can expect some difficult exchanges this week when she and senior ministers discuss the so-called "end state" of the Brexit negotiations for the first time since Britain voted to leave the EU in a referendum in June 2016.
The type of long-term relationship the country should have with the EU is a vexed question at every level in Britain, including within May's cabinet where some want to keep close ties with the EU and others want a more radical divorce from Brussels.
Mindful of the need to keep both sides happy, May has so far plotted a careful path.
Meetings expected to take place on Monday and Tuesday are likely to force those issues out into the open.
One of the key pro-Brexit voices in the cabinet, foreign minister Boris Johnson, has set out his own view ahead of the meetings, warning May that Britain must avoid becoming subordinate to the EU.
"What we need to do is something new and ambitious, which allows zero tariffs and frictionless trade but still gives us that important freedom to decide our own regulatory framework, our own laws and do things in a distinctive way in the future," he told the Sunday Times newspaper.
He said that mirroring EU laws would leave Britons asking "'What is the point of what you have achieved?' because we would have gone from a member state to a vassal state."
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