It's the first time a country has left the European Union so the negotiators - led by former French government minister and European Union commissioner Michel Barnier and Britain's David Davis - will also be navigating uncharted waters.
The government meanwhile said the state opening of the parliament - when May's government presents its legislation programme - will take place on June 21, two days later than planned.
Mr Davis is expected to meet Mr Barnier at the Commission's headquarters in Belgian capital Brussels on Monday but it is not known how long the initial round of talks will last.
"It's entirely up to them", he added less than a week before the Brexit talks are due to start.
Monday's negotiations are to open at 11:00am in Brussels (0900 GMT) with 90 minutes of talks between Barnier and Davis, followed by a working lunch between the pair and a press conference.
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For Brussels, a concern with starting talks on such models would be that Brexit supporters might end up blocking them, raising the risk of time running out to get any deal: "Would you [.] 10 months later find that there was no real majority for that?" the official said.
Barnier this week acknowledged "sensitivity" in London at European Union suggestions that Britain might owe it some 60 billion euros ($66.9 billion) in 2019 and said sorting out the issue soon would help a trade deal: "I would like to very quickly play down this question, and find concrete, pragmatic and just solutions", he said on Monday (12/06).
Mrs May's weakened position in the House of Commons as a result of losing her majority has fuelled speculation the Tories would be forced to soften their stance on Brexit.
In a letter to the European Union last March, Prime Minister Theresa May stated: "The United Kingdom does not seek membership of the single market: we understand and respect your position that the four freedoms of the single market are indivisible and there can be no "cherry picking".
Critics of her approach have urged her to give ground in order to safeguard jobs and the economy.
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"If the government cannot even secure a deal with the DUP, how on earth can they get a deal with the European Union?" asked MP Alistair Carmichael. It does not wash.
If the parties still can not agree a deal by June 29, then the Northern Irish assembly's powers returned to the United Kingdom government.
"Theresa May must immediately create a cross-party joint cabinet committee to negotiate Brexit".
"A little side bargain to keep Theresa May in power. won't have any integrity and certainly isn't as important as the needs of people" in Northern Ireland, said Adams.
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