"Countries including China, Brazil, and the Gulf States have already expressed their interest in striking trade deals with us", she said. "We will go forward understanding we can not be members of the single market", he said on Tuesday.
Asked whether a "No" vote would mean Britain would then rely upon World Trade Organisation terms, she said, "Either way, we will very clearly be leaving the EU".
He joked that his Scottish ancestry meant he liked to "watch my pennies", adding: "I mean I deal in big pennies, that's the problem".
"I want to be clear: what I am proposing can not mean membership of the single market", Ms May told an audience of foreign diplomats and Britain's own Brexit negotiating team at a mansion house in London. "We also want as good, close and trusting a relationship as possible and hope for constructive negotiations with this goal", he said.
As of 3:52 p.m. ET, sterling was on track for its best one-day gain since 2008.
The single market without Britain covers 460 million people.
About 90% of Welsh food and drink is now exported to the EU. British Parliament will decide on any changes to that law after full scrutiny and proper Parliamentary debate.
In a concession to parliamentary critics, the Conservative party leader said lawmakers would also get a vote on any final Brexit agreement negotiated with Brussels.
He said: 'We are seeing an increased number of attacks on Europeans in the UK.
Theresa May has opted for a hard Brexit from the European Union.
The common travel area, operating since the 1920s, allows Irish and British citizens to travel to each others' countries without passport controls.
One objective is making sure the United Kingdom has control over immigration from the rest of Europe. That, May stated, would be impossible if Britain is to fulfil the vows made during the Brexit campaign to take complete control over its borders.
Britons' vote to leave the bloc has opened a huge number of questions about immigration and the future rights of the many European Union citizens already living in the United Kingdom.
In addition, Britain will ensure that workers' rights are fully protected and maintained. And so, pious, pie- in- the- sky dreams of keeping all of the good bits (single market access, financial services passporting, etc.) while doing away with the bad bits (Polish people, mainly) have come to naught: It's a Hard Brexit, baby, with a Capital H.
Sapin said he believed that the apparent lack of a plan to see through Brexit showed that some members of the government "did not want (Brexit) and that it has created debates within the government which are clearly very difficult".
European Union countries accounted for 44 per cent of Britain's total exports in goods and services in 2015, with the country recording a £68.6 billion (US$82.7 billion) trade deficit with the bloc.
And being out of the European Union but a member of the single market would mean complying with the EU's rules and regulations that implement those freedoms, without having a vote on what those rules and regulations are.
"It would to all intents and purposes mean not leaving the European Union at all".
"So we will also welcome agreement to continue to collaborate with our European partners on major science, research, and technology initiatives".
In summation, the twelfth negotiation proposal is for a smooth, orderly Brexit.
'We need to show these people who think that this is the time to deconstruct Europe, to let it fall apart, we have to show them that they are wrong.
"But, I lost that debate - what happens in those countries is critical because it will actually exercise some of these arguments, which we didn't really make in our referendum, about immigration".