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John Springford, deputy director of the Centre for European Reform, a London-based research institute, said that the size of the vote against her “is an even clearer signal that she won’t be able to get her deal through Parliament, and makes it even more likely that when she puts the deal to the vote she will lose that.”

Charles Grant of the Centre for European Reform (CER) suggested May would only secure "very minor changes to her deal". "The substance of the Irish backstop will be unaltered. So I very much doubt that parliament will vote for the deal, when it has the chance to do so," he said.

"She's almost certain to face the challenge," said Charles Grant, director of the Centre for European Reform, a London think tank. "The only consequence of postponing of her Brexit vote is to weaken May's authority several notches further than it already has been."

Charles Grant of the Centre for European Reform think tank said he thinks the upper limit of any extension could be “mid-May” because of the upcoming European Parliament election, but in extremis the EU could be flexible. “Britain’s seats in the European Parliament have already been reallocated and it would be legally complicated to keep the U.K. in the EU beyond the elections,” Grant wrote in a blog for the CER. “But if the EU really wanted to prolong British membership by several months, there could be ways around the European Parliament problem; for example, the U.K. could appoint MPs as MEPs on an interim basis.”

Recent analysis by Sam Lowe of the Centre for European Reform suggests that under the provisions of a free trade agreement between Britain and the EU, UK exports of insurance and pension services will be 19 per cent lower and of other financial services 59 per cent lower. Functions and assets are already moving and the jobs will follow.

"I think there is this kind of empathy for Theresa May," said Agata Gostyńska-Jakubowska, a senior research fellow at the Centre for European Reform. "There is this understanding that she has had this very difficult job, being pressed from both within her party and across the political spectrum. "Some European leaders have recognised her efforts to bring the deal home."

Britain’s exports of financial services to the EU could fall by almost 60 per cent as a result of leaving the single market, marking a “sea change” in the services sector that drives the UK economy, according to new research by the Centre for European Reform.The think-tank sought to assess the impact of new trading barriers on the key areas of services where Britain currently has a comparative advantage — finance, insurance, law and accountancy.