Brussels: EU chief negotiator Michel Barnier said Brexit was a "lose-lose" situation, adding lessons should be drawn from it to understand why people in Britain had voted for it and others across Europe were increasingly drawn to anti-European rhetoric.
Speaking at a European Parliament Committee on Foreign Affairs, Barnier said people were intent on destroying the EU from inside as well as out.
He recalled an exchange with the leader of the Brexit party Nigel Farage, saying he had told him that "after Brexit the European Union will no longer exist."
Barnier said those comments added to the pull of anti-European parties across Europe expressing mistrust and fear of the European project, serving as a warning to the bloc.
"That's why I think we must take good care of the European Union even if we must reform it," he told MEP's.
Barnier cautioned that a no-deal Brexit was more likely by the day, following the UK parliament's renewed rejection on Monday to alternatives to the government's unpopular divorce deal.
He said it was time for Britain to take its responsibilities and choose its Brexit path.
The British Cabinet was scheduled to meet for five hours Tuesday amid calls for compromise to prevent a potentially devastating no-deal exit in just 10 days.
Parliament on Monday rejected four alternatives to British Prime Minister Theresa May's withdrawal agreement, with proposals for a customs union failing by three votes.
In Brussels, Barnier warned that "you either approve the deal to leave in an orderly fashion, and this is the only possible agreement, or you decide to leave without a deal (...) or you ask for extra time but you need to tell us why."
He added: "Is it to hold a referendum? Is it to hold elections? Is it for a cross party political process?" he asked, adding that if an extension was granted the UK would have to hold European elections in May.
"This is mandatory," he stressed.
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The alternative plan that got the most support in Parliament on Monday was a proposal for a customs union, which failed by just three votes. That rejection may be seen positively by May's camp, which will discuss bringing the matter back to Parliament in the Cabinet session.
Exiting the EU without a deal in place would jeopardize trade and travel overnight, with new checks on borders and new regulations on dealings between Britain and the 27 remaining EU nations.