In her speech, the British Prime Minister also said that both sides in the talks must accept that none of them can get "exactly what it wants", but nevertheless, she believes, it is possible to achieve understanding.
"The reality is that we all need to face up to some hard facts", May said.
Against the euro, sterling fell as much as 0.5 percent to 89.47 after trading down 0.2 percent at 89.24 before May gave her a long-awaited speech.
But he rejected suggestions that the United Kingdom would have to accept the fallback option of keeping Northern Ireland in an effective customs union with the EU.
Mr Coveney said if agreement can not be reached during tripartite talks between the UK, Ireland and the EU Commission, the backstop plan of full British alignment with customs union and single market rules that Mrs May "committed clearly" to in December's conclusion of withdrawal negotiations would have to be put in place. They accuse Britain of wanting to cherry-pick benefits of European Union membership without any of the responsibilities.
"We are leaving the single market, life will be different", said Theresa May.
She said: "Crucially, Parliament will be able to take decisions about the rules that are set and so in the circumstances in which, say, the European Union changed a particular rule, there would be a decision for us to take - did we accept it in the future or not?"
May's office says she will say Britain wants to maintain "high standards" of regulation, like the EU's, while having the right to diverge from European Union rules over time.
In a speech Friday outlining her vision for future economic ties, May said: "U.K. and European Union regulatory standards will remain substantially similar in the future".
And May said "bold and creative thinking" could lead to solutions for trade in services and other areas.More news: Jordan Peele is first black screenwriter to win best original screenplay
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May also said Britain wants to remain a member of some European Union agencies, including those governing medicines, chemicals and aviation - and is willing to pay and to play by the agencies' rules.
Tánaiste Simon Coveney also gave an interview to the BBC's Andrew Marr Show and said that while Ms May's keynote speech on Brexit last week - in which she set out her position on the future EU-UK relationship - was welcome, many details were not provided.
"It will provide reassurance to British business and public alike".
Trade lobby group techUK, welcomed the Prime Minister's "pragmatic approach".
Theresa May leaves after delivering a speech about her vision for Brexit, at Mansion House in London.
Britain and the bloc have promised there will be no customs posts or other impediments along the 310-mile (500 kilometer) border.
Marr offered that May has provided some details, noting that 80% of small businesses will "simply be ignored completely" while 20% of very high value goods crossing the border will be dealt with electronically.
Northern Ireland's leader of the Democratic Unionist party, Arlene Foster, welcomed May's commitments to staying out of the customs union, while the Sinn Féin leader, Mary Lou McDonald, said proposals for a "fantasy technological" solution lacked credibility. Effectively Theresa May is trying to state what she wants, whilst also appeasing politicians on all sides of the debate.
"So my message to our friends in Europe is clear". We understand your principles. We understand your principles. we have a shared interest in getting this right.