"So there is responsibility on Britain to ensure that the impact of Brexit on its neighbours is also managed". "We know what we want. So we need to strike a new balance". She said: "Brexit is incompatible with the wishes of the people of the North, acts against our economy and undermines our agreements".
The U.K.is due to leave the 28-nation European Union on March 29, 2019, but the two sides have yet to negotiate new arrangements for trade, security, aviation and a host of other fields.
The DUP leader welcomed the Prime Minister's pledge that one of her five tests for a Brexit deal was "strengthening the Union".
"If this is cherry-picking, then every trade arrangement is cherry-picking", she said.
She dismissed the commission's insistence that it would not allow "cherry-picking" of rights and obligations, insisting that this was a part of any trade negotiation.
But she said that European Union leaders should allow Britain to match regulations in some areas and diverge in others in a "unique and unprecedented partnership".
May, 61, has long kept her cards close to her chest, trying to avoid provoking those in Britain who want a clean break with the European Union, or others who fear the world's sixth-largest economy will suffer if barriers are raised against a major trading partner.
Mr Rees-Mogg praised the Prime Minister's "good" speech, adding: "There are inevitably a few small points that will concern Leave campaigners but we must all recognise that everyone will have to give up something to get a deal, so now is not the time to nitpick". May's speech on Friday was broadly well received in Brussels and at home among the rival factions of her Conservative Party.
The former Business Minister welcomed the PM's speech but added: "This is now a facing up by her...to Brexit reality".
"We must hope that they will be as positive and pragmatic as Theresa May".
Mr Coveney said if agreement can not be reached during tri-partite talks between the UK, Ireland and the European Commission, the backstop plan of full British alignment with customs union and single market rules that Mrs May "committed clearly" to in December would have to be put in place. "Not something that would take 10 years", said New Financial, a think-tank that promotes capital markets in Europe.
Alliance deputy leader Stephen Farry said Mrs May's Brexit speech did "little to address the many contradictions in the UK's Brexit position".
In a speech aimed at answering critics who have accused the United Kingdom government of failing to grasp the tough realities of the exit, May said Britain wanted "the broadest and deepest possible agreement - covering more sectors and cooperating more fully than any free trade agreement anywhere in the world today".
It was also unclear whether Britain having access to the EU's financial markets in return for keeping similar standards to those of the bloc would be accepted in Brussels. "The future of our trading relationship is up there with the most critical issues facing the British farming industry".
"Yes, there will be ups and downs in the months ahead".
'But Parliament would always have the final say and if it wanted to change that and have less market access as a result, that is a trade-off that we would be empowered to make because the sovereignty would reside with Parliament'.