Michel Barnier has warned that the move led by Labour MP Yvette Cooper to block the prime minister from delivering a no-deal Brexit is doomed to fail unless a majority for an alternative agreement is found.

The EU’s chief negotiator, in a speech in Brussels, said the “default” for the UK was still crashing out if MPs could not coalesce around a new vision of its future outside the bloc.

“There appears to be a majority in the Commons to oppose a no-deal but opposing a no-deal will not stop a no-deal from happening at the end of March”, he said. “To stop ‘no deal’, a positive majority for another solution will need to emerge.”

Labour appears set to whip its MPs to back Cooper’s amendment paving the way for legislation that would mandate ministers to extend article 50 if a no-deal Brexit looked imminent.

Barnier said that extending the two years of the negotiating period beyond 29 March should not be the primary focus for the UK parliament.

“We need decisions more than we need time actually”, he said. “I don’t know whether postponing or extending will be raised but its the head of state and government that will have to answer that question by consensus. Some have said to me that if the question is raised, then why would we do that? What would the purpose be? How long would be required?”

There have been growing fears in Brussels that the UK is heading for a crash landing out of the bloc.

EU ambassadors on Wednesday were urged by the European commission to ensure that their national contingency measures did not replicate the terms of today in order to keep the pressure on parliament to forge a “positive majority” for a deal.

Barnier reiterated in his address to the European economic and social committee, (an intergovernmental advisory body comprising workers, employers), and organised civil society, that he believed the key to getting an agreement through parliament lay in the prime minister, Theresa May, embracing a permanent customs union as backed by Labour.

Senior EU diplomats are concerned, however, that this push by Brussels, which would involve redrafting the political declaration on the future relationship accompanying the withdrawal agreement, is falling on deaf ears.

“If the UK red lines were to evolve in the next few weeks or months the union would be ready immediately and open to other models of relationships which are more ambitious”, Barnier said. “We’re ready to rework the content and ambition of the political declaration.”

It is understood that Downing Street’s chief Brexit adviser, Olly Robbins, has been told by EU officials that there was little point in the prime minister returning to Brussels to seek concessions on the Irish backstop.

In an interview with Le Monde, Rzeczpospolita and Luxemburger Wort published earlier on Wednesday, Barnier made public his belief that May’s strategy of trying to secure a time-limit was doomed to fail.

In comments that appear to put a wrecking ball to the prime minister’s strategy, he said the withdrawal agreement in all its facets was the “the only possible option” for Britain as it leaves.

“The question of limiting the backstop in time has already been discussed twice by European leaders”, Barnier said. “This is the only possible option because an insurance is of no use if it is time limited.

“We cannot tie the backstop to a time limit”, he added. “Imagine if your home’s insurance was limited to five years and you’d have a problem after six years … That’s difficult to justify. It’s similar with the backstop.”

The European Parliament will warn on Thursday that it will refuse to ratify a withdrawal agreement that does not contain an “all-weather” Irish backstop, in a further blow to May.

A draft statement from the parliament’s Brexit steering group, seen by the Guardian, further calls for May to offer a new plan for passing the deal next week. The statement says: “The UK government must work together with all political parties in the House of Commons to overcome this deadlock. It expects the UK side to come back as quickly as possible with a positive and viable proposal on the way forward.”

The group of senior MEPs, led by the former Belgian prime minister Guy Verhofstadt, says it expects “greater clarity next week from the UK on its position on the EU-UK relationship for the future”.

Under the backstop, the UK would stay in a customs union with the EU unless an alternative arrangement could avoid the imposition of a hard border on the island of Ireland.

In her statement to the Commons on Monday, May had said she would seek further concessions from Brussels having acknowledged that a large number of Conservative and Democratic Unionist party MPs “fear that we could be trapped in it”.

The Tory MP and Brexiter Andrew Murrison has resubmitted a “sunset clause” amendment in the Commons, which offers support for May’s deal if the backstop can be time-limited to the end of 2021.

It is believed that the prime minister may encourage Tory MPs to back the amendment next week if the Speaker, John Bercow, chooses to put it to a vote, then return to Brussels with “proof” of what is needed to get the deal through, should it pass.

Barnier told the European media outlets that he did not believe this was the key to success in parliament.

“Things could start moving rapidly”, Barnier said. “This depends on the future relationship, like I already said. We are ready to be more ambitious if the British decide to shift their red lines, for example by remaining in a customs union, or participating in the single market. I believe there is a readiness in London for that.”

On Wednesday, Barnier and EU officials also back-pedalled on their claims over the last 24 hours that a no deal Brexit would “obviously” lead to the imposition of a hard border on the island of Ireland.

“We will have to find an operational way of carrying out checks and controls without putting back in place a border”, Barnier said, in a sign of the sensitivity of the issue.

• This article was amended on 24 January 2019 to more fully describe the European economic and social committee.