Nearly a year after Britain voted to leave its biggest market, the talks come amid signs the U.K.is softening its approach to the split and adopting a more conciliatory tone.
Full negotiations had been due to start on June 19, but Brussels said the date was still not confirmed after British Prime Minister Theresa May unexpectedly lost her majority in parliament.
Her spokesman said Britain would not change its stance on Brexit, though May told her lawmakers she would seek a broader consensus in the party on her approach.
The talks also gave her the opportunity to try to reassure the other parties that a tie-up with the DUP would not compromise Britain's impartiality in the delicate Northern Ireland peace process.
"Their position on this was very similar to the Conservative position according to their manifesto".
Following talks in Dublin with the new Irish Prime Minister Leo Varadkar, she said that reaching a "sensible" Brexit had been the focus of their talks.
"We want to end the anxiety facing 4 million citizens", he said.
Brexit Secretary David Davis will meet with the European Commission's chief negotiator Michel Barnier at 11am local time in Brussels on Monday to begin more than seven hours of official talks. "And so it's my expectation that it will take place", he added.
"Theresa May must immediately create a cross-party joint Cabinet committee to negotiate Brexit".
Liberal Democrat MP Alistair Carmichael said: "The Conservatives can not go from weak and wobbly to business as usual in three days".
The prospect of Brexit has sent a wave of concern through Britain's business sector.
Brussels has previously warned the UK Government it will only enter talks on a potential future trade deal with Britain once "significant progress" is made on divorce matters.
The spokesman said the UK's "first aim" was to move ahead on securing the rights of European Union citizens in the United Kingdom and UK citizens living in the EU.
The UK has agreed to sort out its European Union "divorce bill" and citizens' residence rights before starting Brexit trade talks, European Union sources have told the BBC. "That is why we are pushing ahead with negotiations on Monday".
European Commission First President Frans Timmermans told the Prague event that the EU would be happy to see the United Kingdom change its mind and stay in the bloc.
"In my experience recently, businesses that look over the garden fence have gone: "Hmm, (the) grass is not quite as dark and unforgiving as you might expect", Andrew told the BBC.