He offered to add wording to a non-binding ‘declaration’ accompanying the deal, that sets out the parameters for negotiating a future trade deal, promising “to be more ambitious in terms of content and speed” on that future deal.

However this is unlikely to satisfy the Brexiteers in May’s party who voted to reject the Prime Minister's deal in January.

May and Juncker agreed to meet again before the end of February to “take stock”.

Juncker also pointed out that any change to the deal, including the declaration, would have to be agreed by the European Parliament and all 27 other EU nations.

Though May publicly insists Brexit will meet its March 29 deadline, senior ministers are reportedly saying privately that they would prefer to extend that deadline – which would require the consent of the EU nations – rather than plunge into a ‘no-deal’ Brexit with resulting problems at the borders and damage to industry.

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May had told the House of Commons, after it overwhelmingly rejected her deal, that she would seek legally binding changes to the Brexit withdrawal deal.

Specifically, she said, she wanted those changes to address concerns – mostly within her own party – that the deal would potentially trap the UK in an unwanted customs union with the EU under the terms of a ‘backstop’ negotiated to keep the Irish border free of checkpoints.

The backstop would come into effect if a new trade deal was not done within the next few years, and if no alternative has been agreed.

Hardline Brexiteers have insisted the backstop be removed from the Brexit Withdrawal Agreement altogether, to be replaced with “alternative arrangements” based on technology.

However they were rebuffed by May herself earlier this week when she visited Northern Ireland. Though technology could “play a part” in keeping the border free of checkpoints, May said she was looking at changes to the backstop “to introduce a time limit or create an exit mechanism”.

“I’m not proposing to persuade people to accept a deal that does not contain that insurance policy for the future,” she said on Tuesday.

She also affirmed her “unshakeable” commitment to delivering a Brexit “that ensures no return to a hard border between Northern Ireland and Ireland”.

The change infuriated Brexiteers who had been pushing a so-called Brexit ‘Plan C’ that relied on technology-based customs checks away from the border – despite EU officials saying they had already examined such suggestions and considered them unworkable in the time available.

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May was due later on Thursday to meet European Parliament president Antonio Tajani and the Parliament's Brexit coordinator Guy Verhofstadt.

She was also expected to hold talks with European Council President Donald Tusk, who on Wednesday declared there was a “special place in hell” for those who campaigned for Brexit without a plan to deliver it safely.

Meanwhile, Opposition Leader Jeremy Corbyn set out new conditions under which Labour would support a Brexit deal.

His five demands included a “permanent and comprehensive UK-wide customs union” with aligned with EU rules, wide participation in EU agencies and programs, and close alignment with the EU single market.

He appears to have scrapped a previous demand that any deal must deliver the “exact same benefits” as staying in the current EU single market and customs union.