Mrs May's critics say such a proposal would make Britain a rule-taker with no say in forming future regulations.
The issue of migration continues to be a highly contentious one, with control over borders to end free movement of people from member-countries having played a crucial part in the campaign for leaving the European Union in the June 2016 Brexit referendum.
The border between Ireland and Northern Ireland is one of the biggest sticking points in European Union negotiations, but ahead of a meeting with the Prime Minister on the subject of the talks, Foster said her party will not soften its stance.
Delegates stood in line for up to two hours to hear him urge the party to "follow our conservative instincts" by cutting taxes to stimulate growth.
May has had a tough year since a disastrous 2017 conference speech, when she was her plagued by a cough and interrupted by a prankster while parts of the backdrop fell down as she was speaking.
British Prime Minister Theresa May says her Conservative government plans to scrap years of cost-cutting austerity policies introduced after the 2008 global financial crisis.
The DUP leader delivered a speech at the event that attempted to chart a middle-ground of respect for LGBT+ rights while defending her stance against same-sex marriage.
Manuel Pellegrini sends message to West Ham United fans on Twitter
United is on pace to lose 16 Premier League matches, which would put it woefully short of qualifying for the Champions League. Shaw's gesture was certainly appreciated by the United away fans, who had very little to cheer about at the London Stadium.
May, who landed the top job by an "odd chance" to borrow the Economist's less than charitable phrase (even though she personally voted Remain) sadly is neither extraordinary nor is she transformative.
When the Prime Minister did speak of Brexit, it was without referring once to her Chequers soft-Brexit plan by name, a sign that she has now accepted the term has now acquired a tox status.
The crucial conference speech could be a make or break moment for Mrs May as she battles to push through a Brexit deal. For many Conservatives, whose party is dwindling in numbers and divided over Brexit, he was a tonic.
"We don't want to see any border on the Irish Sea but the commitment to an Irish backstop of last December is very clear", Coveney said, referring to the "insurance policy" backstop arrangement all sides agreed to in principle over how to retain an open border on the island of Ireland after Brexit.
The EU and Union flags. "But we need to be honest about it. Leaving without a deal - introducing tariffs and costly checks at the border - would be a bad outcome for the United Kingdom and the European Union".
Michel Barnier has said customs controls on goods going between Great Britain and Northern Ireland could be kept light touch, through scanning technology and pre-clearance. "It delivers the referendum, it keeps faith with the British people".