Approved by a national referendum in June, Britain's EU departure -- informally known as Brexit -- "is not about the UK suddenly wanting to be inward looking," Britain's new leader said in her first major interview since taking office. "Actually we will continue to be a bold, out-looking country"
May's televised comments were made before leaders of the world's most industrialized nations gathered in Hangzhou at the G20 summit this weekend to discuss top issues, including the global economy. The G20 includes 19 of the world's major economic powers plus the European Union.
She said her administration wants to "emphasize the role that we would be playing in the world" including forging new deals. "We want to be an independent Britain, forging our own way in the world."
"I am not going to pretend that it is all going to be plain sailing," May added. "I think we must be prepared for the fact that there may be some difficult times ahead, but what I am is optimistic."
During scheduled meetings with President Obama, May said she wants "to start to scope out what the negotiations on a trade deal would look like, so when the time comes, when we are ready to sign those deals, we can do so."
Obama said Sunday he wanted to gauge the new leader's plans during their meetings. The US has insisted the UK's departure from the EU must proceed in an organized fashion. The "special relationship" between the US and the UK would guide Washington's view of the process, he said.
"The bottom line is that we don't have a stronger partner anywhere in the world than the United Kingdom," said Obama. "Despite the turbulence of political events over the last several months, we have every intention to making sure that that continues."
The weekend summit is Obama's first face-to-face encounter with May since she replaced David Cameron, a close Obama ally who resigned after the Brexit vote. Obama took the unusual step of personally lobbying against Britain's UK exit. After the vote didn't go his way, the President said he would stand by Britain amid the country's internal struggles.
During a joint news conference with Obama on Sunday, May said exit negotiations would move forward.
"Brexit does indeed mean Brexit," she said, using the slogan she coined after taking office in July.
In the BBC interview May repeated several times that she and her party "respect the wishes" of the British electorate. "The British people want us to leave the EU and that is what we would do."
About a Scottish referendum to leave the UK
On the possibility that Brexit might prompt a second Scottish referendum to leave the UK, May explained, "I don't think there is a question of whether there could be a second Scottish referendum, it is a question of whether there should be a second referendum."
In her comments, she cast distinctions between's Scotland's 2014 referendum and the larger vote by the UK to exit the EU. In that 2014 vote, 55% of Scottish voters cast ballots in favor of remaining in the United Kingdom.
She said Scotland wasn't the only part of the UK that overall voted to remain. "But the overall view of the UK was to come out of the EU."
Scotland is one of four countries that make up the United Kingdom. England, Wales and Northern Ireland are the others. Scottish voters overwhelmingly backed remaining in the EU, with 62% in favor and 38% who wanted to leave.
Days after the referendum, Scottish First Minister Nicola Sturgeon said her government would begin preparing legislation for a new vote that could be held before the UK formally leaves the EU.
She said in June it appeared unlikely that UK leaders would try to block the effort, saying it is "highly likely" that a new independence referendum will be held.
On Britain's economy
On the British economy she told the BBC: "We have had some good figures and better figures that some had predicted would be the case, but what is important for us now is that we maintain that policy of ensuring economic stability and a strong economy for the future.
Part of that is going to be -- as we come out of the EU -- ensuring we have trade deals around the world," May said. "I want the UK to be a global leader in free trade."
Regarding immigration, May said Bexit vote sent a "very clear" message from the British people "that they don't want free movement to continue in the way that it has done in the past. They don't want to see controls of people coming in from the EU. "
When asked about the rights of EU foreigners living in the UK, May said, "I expect to be able to guarantee their status for the future, but the only circumstances where that wouldn't be possible would be if the status of British citizens living in other EU countries was not guaranteed."
Boris Johnson: We welcome more Polish immigrants
Separately, UK's Foreign Secretary Boris Johnson, one of the leading voices in the Brexit campaign, said Britain looks forward to welcoming a new generation of Polish immigrants, according to the Guardian
Johnson spoke to reporters after visiting a British Council language school in the Polish capital of Warsaw on Saturday, the Guardian reported.
The foreign secretary only briefly alluded to the killing of a 40-year-old Polish man in Harlow. Factory worker Arek Jozwik died after being attacked late last month in an open air shopping center in the town, northeast of London. Poland has launched an investigation into the murder, which authorities there believe could be a hate crime.
Police in Britain have recorded a dramatic rise in racist attacks
in the wake of Brexit, with five times the usual number of incidents reported after the country voted in a June referendum to leave the European Union.
"London is the most welcoming, multicultural, happening city on Earth -- no disrespect to Warsaw -- and there is no room for xenophobia," Johnson said during a media appearance alongside his Polish counterpart Witold Waszczykowski.
Johnson made the short stopover in Poland on the way back to the UK after attending the EU foreign ministers' meeting in Slovakia.