Speaking to BBC television – in her first major interview since taking office – May also ruled out a new general election anytime soon, saying Britain needed stability following June's referendum vote to pull out of the European Union.
She voiced optimism about the health of Britain's economy but warned that there could be tough times ahead.
"I'm not going to pretend that it's all going to be plain sailing," she said. "I think we must be prepared for the fact that there may be some difficult times ahead. But what I am is optimistic."
She insisted the country would "make a success" of leaving the EU, saying she was also "optimistic" about new opportunities for Britain outside the EU.
The PM said she wanted "an independent Britain, forging our own way in the world".
May, who took office in July after David Cameron quit, following the referendum, also confirmed Downing Street briefings that she is not intending to call a general election soon.
This is despite the ruling Conservative party having only a small majority in the House of Commons, which could make it hard to pass controversial laws, and Jeremy Corbyn's deeply divided opposition Labour Party lagging in opinion polls and holding a leadership contest.
"I'm not going to be calling a snap election," May said.
"I've been very clear that I think we need that period of time, that stability, to be able to deal with the issues that the country is facing and have that election in 2020."
She told the BBC she wanted to "start to scope out" with them how future trade deals would look post-Brexit.
European Commission chief Jean-Claude Juncker said Sunday he opposes trade negotiations between Britain and other nations while it remains part of the bloc after Australia said it was about to launch talks on the issue.