The PM has promised to push for the “freest possible trade” with European countries and warned the EU that to try to “punish” the UK would be “an act of calamitous self-harm”.
She also said Parliament would vote on the final deal that is agreed.
Labour warned of “enormous dangers” in the prime minister’s plans.
And the European Parliament’s lead negotiator said there could be no “cherry-picking” by the UK in the talks.
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.
Negotiations are set to begin after notice under Article 50 of the Lisbon Treaty is served by the end of March.
It was not her intention to “undermine” the EU or the single market, Mrs May said, but she warned against a “punitive” reaction to Brexit, as it would bring “calamitous self-harm for the countries of Europe and it would not be the act of a friend”.
She added: “I am equally clear that no deal for Britain is better than a bad deal for Britain.”
But the most keenly awaited part of the speech dealt with the UK’s post-Brexit trading relationship with the rest of Europe.
Any agreement with the EU must “allow for the freest possible trade in goods and services”, Mrs May said.
“But I want to be clear: what I am proposing cannot mean membership of the single market.
“It would, to all intents and purposes, mean not leaving the EU at all.That is why both sides in the referendum campaign made it clear that a vote to leave the EU would be a vote to leave the single market.”
EU leaders have warned that the UK cannot access the single market, which allows the free movement of goods, services and workers between its members, while at the same time restricting the free movement of people – and the PM has pledged to control EU migration.
Mrs May also indicated the UK’s relationship with the customs union – under which EU countries do not impose tariffs on each other’s goods, while all imposing the same tariff on goods imported from outside the EU – would change.