European Commission chief Ursula von der Leyen warned Wednesday that failing to rapidly negotiate a new trade deal after Brexit would hurt Britain more than it would the EU.
"The timetable ahead of us is extremely challenging," she told the European Parliament in Strasbourg.
"In case we cannot conclude an agreement by the end of 2020, we will face again a cliff edge. This would clearly harm our interests but it will impact more the UK than us."
Eurosceptic British MEPs laughed at the warning, but it reflects a pessimistic mood among Brussels officials.
"Time is limited and it won't be possible to do everything, but we'll do everything we can. We can't do it all but we will give it our all," EU Brexit negotiator Michel Barnier said.
"After the transition period we'll have to continue to work with the British and to negotiate," he said.
Britain is due to leave the European Union on January 31, but will remain in a transitional arrangement until the end of the year while negotiators debate future trade ties.
Under the withdrawal agreement which Prime Minister Boris Johnson has agreed with Europe but not yet pushed through parliament, the UK could ask for a one or two year extension.
But Johnson, who last week won a comfortable majority in the UK general election, insists he will not ask for more time and is preparing legislation to forbid such a move.
In this case, negotiators will only have 11 months to conclude a trade agreement, a task that officials on both sides have warned is extremely ambitious.
And if 2020 comes to an end with no deal concluded, Britain will sever ties with the huge EU single market with no follow-on deal to protect jobs and trade on both sides.
"We will organise these negotiations to make the most out of the short period. On February 1 we will be ready to propose a mandate for the negotiations," von der Leyen said.
"I hope... that we will have an unprecedented partnership. This is not the end of something. It is the beginning of new relations between neighbours and I want us to become good neighbours with our friends in the UK. Long live Europe."
The new British parliament, dominated by Johnson's Conservative Party, is expected to to pass his withdrawal bill quickly, but the European Parliament will gave to ratify it on January 29.
This is widely expected to be a formality, but on Tuesday the chairman of its Brexit steering group, former Belgian premier Guy Verhofstadt, said it would not be a rubber stamp.
"I get thousands of mails from UK citizens living in the EU and EU citizens living in the UK who are panicking and wanting to know their status," he said.
"That will have to be resolved before we approve the exit treaty," he said, calling on Johnson to guarantee the residence rights of all EU nationals with "no ifs or buts".
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