The president of the European Commission, Jean-Claude Juncker, has claimed Britain "underestimates" the complexity of Brexit talks.
Speaking after the remaining 27 EU states unanimously agreed their strategy for Brexit negotiations , Mr Juncker said discussions over EU citizens' rights would take "a huge amount of time".
He said the Commission had drawn up a proposed agreement on the issue "which could be adopted immediately if our British friends would be ready to sign it (but) that will probably not happen".
Mr Juncker added: "I have the impression sometimes that our British friends… underestimate the technical difficulties we have to face.
"The single question of citizens' rights is in fact a cortege of 25 questions that have to be solved."
Hitting out at Theresa May over her stance during their talks this week at No 10 , he said: "Every time I was asking questions she told me to be patient and be ambitious.
"The same remarks have to be addressed to the UK".
Mr Juncker went on to say the Downing Street meeting was "excellent", before joking: "I'm not talking about the food".
He said: "Privately everything went well but we have a problem, the British want to leave the EU and it's not feasible that it can be done just like that."
Speaking alongside Mr Juncker at a summit in Brussels, European Council President Donald Tusk called on the Government to provide a "serious response" on the issue of EU citizens' rights.
He also hailed the "outstanding unity" of EU leaders who endorsed draft negotiating guidelines in under a minute.
Under the terms of the EU strategy, Britain must settle its so-called divorce bill and reach agreement on the rights of EU citizens living in the UK before negotiations can move to trade talks.
This puts the EU on a collision course with No 10, as Mrs May has said she wants to negotiate a new trade deal at the same time.
The strategy also states that the Prime Minister has to reach an agreement on the Irish border and provide clarity over the status of EU law within the withdrawal phase.
Following the summit, several European leaders indicated that the Commission would take a hard line during talks.
Luxembourg's prime minister, Xavier Bettel, accused the Prime Minister of attempting to cherry-pick a Brexit deal.
He said: "Before you had the soft Brexit and the hard Brexit, and in future maybe you will have Theresa's Brexit, so maybe that is the reason she organised the elections."
Meanwhile, Belgian prime minister Charles Michel said Britain might attempt to "split the 27 nations and it is a trap we need to avoid".
He added: "If you are no longer part of a club, it has consequences. A Brexit for free is not possible."
Brexit talks are expected to begin after the General Election on 8 June.