The president of the European Commission has said he is “not very optimistic” that a no-deal Brexit can be avoided, following a meeting with Theresa May in Brussels.

Jean-Claude Juncker said recent events had suggested there was no majority in favour of a deal in the British parliament.

The meeting with the prime minister appears to have failed to reassure Brussels that Ms May has control of the political situation – a perception made worse by the Conservatives’ loss of a trio of MPs on Wednesday.

“If no deal were to happen, and I cannot exclude this, this would have terrible economic and social consequences in Britain and on the continent, so my efforts are oriented in a way that the worst can be avoided. But I am not very optimistic when it comes to this issue.”

“Because in the British parliament every time they are voting, there is a majority against something, there is no majority in favour of something,” Mr Juncker told a session of the European Economic and Social Committee.

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Ahead of yesterday’s meeting Mr Juncker said he did not expect a breakthrough. Senior Tories were reportedly upbeat however, trailing the prospect of the prime minister returning to London with concessions, but the message was not matched by officials in Brussels.

The UK government wants the EU to make legal changes to the Irish backstop policy, which Brexiteers are implacably opposed to in its current form. However the EU says the backstop is necessary to preserve the peace process in Northern Ireland.

Behind the scenes, EU officials are sceptical that anything they could offer would be enough to placate Tory rebels. Instead, Brussels figures have suggested the prime minister should try to work with Labour to construct a deal the opposition party could back.

To that end, Jeremy Corbyn visited Brussels on Thursday for meetings with Michel Barnier, the EU chief Brexit negotiator, and his team. He told reporters in Brussels the talks were “useful and informative”.

Mr Corbyn said the meeting had left him in no doubt that people across the EU were “absolutely exercised” about the threat of no deal and that it needed to be taken off the table.

A joint statement by Ms May and Mr Juncker after talks broke up late on Wednesday said the pair discussed what extra reassurances could be given to MPs, and “both reconfirmed their commitment to avoiding a hard border on the island of Ireland and to respect the integrity of the EU’s internal market and of the United Kingdom”.

Speaking on her way out of the meeting, the prime minister told reporters: “I’ve had a constructive meeting with President Juncker this evening. I’ve underlined the need for us to see legally binding changes to the backstop which ensure it cannot be indefinite, that’s what is required if a deal is going to pass the House of Commons.

“We’ve agreed that work to find a solution will continue at pace, time is of the essence and it’s in both our interests that when the UK leaves the EU it does so in an orderly way. And so we’ve made progress and the secretary of state for exiting the EU, the Brexit secretary, and the attorney general will be in Brussels tomorrow for further talks.”