Brexit: UK to leave single market, says Theresa May
But the prime minister promised to push for the "freest possible trade" with European countries and to sign new deals with others around the world.
But Labour warned of "enormous dangers" in the prime minister's plans.
Mrs May used her much-anticipated speech to announce her priorities for Brexit negotiations, including maintaining the common travel area between the UK and Irish Republic and "control" of migration between the UK and the EU.
Mrs May said there would not be a "blow-by-blow" account of negotiations, set to begin after Article 50 of the Lisbon Treaty is invoked by the end of March.