EU President Donald Tusk said on Tuesday that the outcome of fraught Brexit talks was "up to London" and that abandoning the EU divorce remained an option for the UK.

"The EU will be able to rise to every scenario as long as we are not divided," Tusk told MEPs at a session of the European Parliament in the eastern French city of Strasbourg.

"It is in fact up to London how this will end: with a good deal, no deal or no Brexit," he said, reiterating the controversial idea that the EU was open to backtracking on Britain's decision to leave the bloc.

"We have managed to build and maintain unity among the 27 (remaining EU members), but ahead of us is still the toughest stress test," said former Polish prime minister Tusk.

The comments come just days after European Union leaders threw British Prime Minister Theresa May a lifeline in Brexit talks, agreeing to start preparations for the next stage of negotiations on post-Brexit trade and a transition deal.

Commission chief Jean-Claude Juncker, also in European Parliament, strongly underlined that the commission, which handles the talks for the EU, was approaching the negotiations in good faith.

"The commission is not negotiating in a hostile mood," said Juncker, who on Monday had to firmly deny a media report saying May begged him for help in the talks.

"We want a deal. Those who don't want a deal, the no dealers, they have no friends in the commission," said Juncker.

The slow progress in the two years of Brexit talks has stoked fears Britain could leave the European Union in March 2019 without a deal in place, risking economic and legal chaos.

May is meanwhile struggling to contain divisions within her government and the belief among Brexit hardliners that Britain can afford to take a tough stance with Europe.