This ‘hard Brexit' stance is a stark contrast to Switzerland's recent decision to water down a publicly-voted initiative to limit immigration from the EU.
Instead of imposing immigration quotas the Swiss parliament chose a ‘light' solution which did not contravene the EU's essential principle of free movement of people. In doing so they could maintain the country's raft of bilateral agreements with the bloc.
The decision reached by the Swiss parliament in December after nearly three years of wrangling was deemed anti-democratic by some, since never before had a new law diverged so far from the text of an initiative approved by the public in a legally-binding referendum.
But parliament defended itself by saying although the people voted for immigration curbs, they did not vote to end Swiss-EU bilaterals.
A contrast to the softly-softly tone employed by the Swiss government in the past few years, May's tough talking on Wednesday was well received by some politicians in Switzerland who opposed the Swiss deal.
Speaking to Le Tribune de Genève Roger Köppel of the Swiss People's Party – which spearheaded the anti-immigration initiative and opposed its ‘light' implementation – praised the British leader.
“She wasn't personally in favour of Brexit. But she takes democracy seriously and applies the popular mandate, in contrast to the Federal Council,” he said.
May gained praise from left-wing politicians too, with Socialist Party MP Roger Nordmann telling the paper her position was logical.
“Unlike the Federal Council she hasn't claimed that we can have our cake and eat it too. To limit immigration she will come out of the single market,” he said.
But he added that May's decision “indirectly backs up the position of the Swiss parliament which, for its part, also made another clear choice: to preserve the bilaterals.”
Reaction in the Swiss press was sceptical, with Le Temps saying the British PM's plans to come out of the single market but renegotiate some sort of trade agreement were a “daydream”.
“She will only take from the announced separation without giving compensation or concessions.... She imagines an island whose empire will be the world but without the unsolvable problems posed by the colonies of the old Empire with their undesirable migrants that London doesn't know how to refuse,” it said.
The Tages Anzeiger was also cynical, saying May had asked what sort of country we want to be and “unfortunately her reply was rather sour”.
Brexit does not give her a mandate to change the direction of the nation, it said.
“Yes the people voted. But not about all the things that May sells as the future of the country.”
May followed her Brexit speech by travelling to Switzerland to speak at the World Economic Forum in Davos on Thursday.