The leaders of the other 27 countries will stress that Britain will be liable for costs for at least a year after it leaves in 2019, according to the draft negotiating guidelines seen by AFP.
They insist that Britain's huge finance industry must also stick to EU rules if it wants easy access to European Union markets.
And Britain should give EU citizens permanent residency after living there for five years, they say, in a challenge for the British government which has vowed to limit immigration.
The leaders are also expected to have a "wider debate on Brexit and the upcoming talks" at the summit, a European source told AFP.
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The EU's language has notably toughened from EU President Donald Tusk's first draft, issued two days after British Prime Minister Theresa May triggered the divorce process on March 29.
The new harder stance comes as May prepares to hold talks with European Commission chief Jean-Claude Juncker and Barnier in London on Wednesday.
Previously it only mentioned costs up to Britain's withdrawal in 2019, but the new version spells out the EU belief that Britain is liable for all costs it signed up to while a member.
Britain's prized financial services industry is also targeted, with changes to the draft making it clear that arrangements for it will not necessarily be tied to any future trade deal with the EU.
The EU has meanwhile made a top priority of protecting the rights of three million European citizens living in Britain and one million Britons living in Europe, who currently can work and live anywhere they choose in the EU.
But the latest draft adds a new demand for EU citizens to have "the right to acquire permanent residence after a continuous period of five years of legal residence" -- a move that is likely to be opposed by London.