The GBP plunged after Brexit comments by May.
Theresa May has revealed little about her strategy for pulling Britain out of the European Union.
But comments made Sunday by the prime minister suggest that exit negotiations will be exceptionally painful.
The one priority that May has marked out - limits on EU migration - implies that British companies will face new barriers in selling goods and services to hundreds of millions of consumers in Europe.
"We will outside the European Union be able to have control of immigration and be able to set our rules for people coming to the U.K. from member states of the European Union," May said in an interview with Sky News on Sunday, her first TV interview of 2017.
The prime minister's position runs counter to rules that require all members of Europe's single trading market to allow free movement of people across their borders.
Top EU officials, including German Chancellor Angela Merkel and European Council President Donald Tusk, have said they will not allow Britain to remain a member of the single market without playing by its rules.
May did not directly address a series of questions on whether Britain would be leaving the single market. "Anybody who looks at this question of free movement and trade as a sort of zero sum game is looking at it in the wrong way," May said.
But she flagged clearly that her objective was a clean break with the U.K.'s biggest trading partner.
"Often people talk in terms as if somehow we are leaving the EU, but we still want to keep bits of membership of the EU," she said. "We are leaving. We are coming out."
The government was last week accused of "muddled thinking" by its own ambassador to the European Union, who resigned less than three months before exit talks are set to begin.
"We do not yet know what the government will set as negotiating objectives for the U.K.'s relationship with the EU after exit," Ivan Rogers wrote in a goodbye note to staffers.
"Our thinking on this isn't muddled at all," she said. "There hadn't been any plans made for Brexit so it was important for us to take some time to actually look at the issues, look at the complexity of the issues."
Meanwhile, the leader of Scotland's government, Nicola Sturgeon, repeated her pledge to hold a referendum on Scottish independence if the U.K. leaves Europe's single market as a consequence of Brexit. Scots voted by a clear margin in favor of remaining in the EU in the June referendum.
"They will be making a big mistake if they think that I am in any way bluffing," she said Sunday. "We now face being taken out of the EU. That creates a much more fundamental question for Scotland."