The Prime Minister said she will try and reach a free trade deal with the bloc that means we will no longer have to contribute "huge sums" to the EU budget.
In a speech this morning, the Prime Minister said that her main priorities for Brexit negotiations include: maintaining the common travel area between the UK and Ireland, tariff-free trade with the EU and 'control' of immigration rights for EU citizens.
Director of the Liberal Democrat Christian Forum and remain campaigner Sarah Dickson told Premier News Hour that it's unlikely that other EU states will accept all of the UK's demands.
Dickson said: "The speech to me sounded like Theresa May was saying we want all the benefits but not any of the costs and I'm not sure the other 27 EU member states will look so favourably on the EU negotiations."
She added that she felt the public had been misled over the issue of the single market in the run up to the referendum.
"It was said throughout the EU campaign generally that if we left the EU that that wouldn't mean leaving the single market - particularly not leaving the customs union as well which will be really impactful to business in the UK that import and export to our neighbours," Dickson said.
But Tory MP and leave campaigner David Burrowes told Premier that he thought that the speech was very positive for the future of the UK.
"We will be regaining control of our laws, our borders and our money and that means inevitably that we will not be a part of the single market," Burrowes said, "It was a firm but clear speech that showed we are back in control of our destiny."
Questioned about Mrs May previous comments that we'd be worse off leaving the single market before the referendum, Burrowes said things have changed.
"The world has moved on, we've had a referendum and she is fulfilling the mandate set before her."