The Prime Minister hailed their decision as “an important step” towards a “smooth and orderly Brexit”.
But within an hour of the announcement, EU chiefs claimed detailed trade talks will not begin until March and demanded that Britain remains signed up to EU rules for an extra two years.
It came in a document setting out guidelines for the next round of negotiations published by EU Council President Donald Tusk.
The document said the UK must accept a continued open door to EU migrants, meddling by the EU’s Court of Justice and a ban on trade deals with other countries for a full two-year transition period after formally leaving the EU in March 2019.
Whitehall sources angrily hit back by warning that the Prime Minister would not put up with any “backsliding” or attempts to “freeze up” the talks.
German Chancellor Angela Merkel warned that the next round of negotiations will be “tougher” than the first.
The opening of diplomatic hostilities in the second phase of talks threatened to overshadow the Prime Minister’s achievement in breaking the deadlock to conclude the first round.
Mrs May was applauded by European leaders after delivering a speech at the summit dinner on Thursday night.
Commission president Jean-Claude Juncker praised her as a “tough, smart, polite and friendly negotiator”.
Speaking in her Maidenhead constituency after returning from Brussels yesterday, Mrs May said: “There is still more to do but we are well on the road to delivering a Brexit that will make Britain strong, prosperous and secure.”
She said talks on Britain’s future relationship with the EU would begin straight away. But campaigners were furious about the apparent delay.
John Longworth and Richard Tice, co-chairmen of the Leave Means Leave pressure group, said: “There are concerning reports that the EU will not start negotiations until mid-February at the earliest. This is unacceptable.”
Gisela Stuart, chairman of the Brexit-backing Change Britain campaign, said: “It’s baffling why trade talks must wait until March. Brussels has had plenty of time to prepare.”
In a joint statement, employers organisations warned: “Further delays could have damaging consequences for business investment and trade.”