May hosts European Commission President Jean-Claude Juncker and chief negotiator Michel Barnier at Downing Street for the first face-to-face talks since her historic triggering of the two-year withdrawal process.
The encounter comes as the EU has toughened its strategy, making new demands over financial services, immigration and the bills Britain must settle before ending its 44-year-old membership in the bloc.
The latest draft negotiating guidelines, agreed on Monday by Barnier and European diplomats, point to months of difficult talks ahead as the EU seeks to ensure Britain does not get a better deal outside the bloc than inside.
According to the document, seen by AFP, the other 27 EU countries will seek to hold Britain liable for the bloc's costs for at least a year after it leaves in 2019 -- longer than was previously proposed.
Britain will also be required to give EU citizens permanent residency after living there for five years, in a challenge for the government, which has vowed to limit immigration.
And the guidelines recommend that Britain's dominant finance industry will not necessarily be tied to any future trade deal with the EU and that it must also stick to the bloc's rules if it wants easy access to EU markets.
On the other side, May is seeking to shore up her mandate for the Brexit talks by calling a snap election for June 8, with polls suggesting her Conservatives will return with an increased majority.
She has committed to pulling Britain out of Europe's single market to end free movement of EU citizens into Britain, but says she wants to form a new partnership with the bloc.
May's spokesman said the visits show that Britain "will be approaching the negotiations in a constructive manner and with great goodwill".
But Nina Schick, associate director at advisory firm Hanbury Strategy, told AFP there was in a sense in Britain of "at best optimism, at worst just not understanding where the EU side is coming from."
The leaders of the other 27 EU nations will meet on April 29 to set down the bloc's red lines, though the talks will not begin until June.
Schick, who works with the Open Europe initiative, said that the tougher guidelines "are not really a surprise" and that both sides were likely to "reiterate their positions" at the Downing Street talks.
May has already held talks with senior EU figures, including European Parliament President Antonio Tajani and European Council chief Donald Tusk, who visited Downing Street on April 6.
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