LONDON (Reuters) - Pro-EU lawmakers threatened on Wednesday to withdraw their support for Prime Minister Theresa May’s Brexit strategy if she does not follow through on concessions they thought they had been promised.

Anti-Brexit demonstrators wave Union and EU flags opposite the Houses of Parliament in London, Britain, June 12, 2018. REUTERS/Simon Dawson

On Tuesday, rebels in May’s party who want parliament to have more say over the final outcome of negotiations on leaving the European Union extracted a major concession from the government in exchange for not voting against their leader.

The government agreed to discuss elements of a rebel plan to create new checks and balances on the Brexit deal, and where possible incorporate them into the laws that will formally end Britain’s EU membership.

But, the pro-EU MPs’ version of what they were promised appears to differ from what they government says it offered, threatening to reignite the dispute and reviving the possibility of a revolt that would badly damage May’s authority.

The disagreement centres on whether the government agreed to consider a specific clause of the rebel proposal that would hand parliament control of the Brexit process if ministers are unable to strike an exit deal by Feb. 15, 2019.

Some lawmakers say this is what they were promised; the government is less clear and has made statements apparently to the contrary.

“If the PM goes back on that there will be no agreed amendment that I can support #sortitplease,” leading pro-European lawmaker Anna Soubry tweeted.

Speaking in parliament on Wednesday, May said the government could never allow the hands of the government to be tied in the negotiations or allow the Brexit decision to be reversed.

Asked if the prime minister’s words ruled out a discussion on the contentious rebel clause, her spokesman said: “I think that is a fair assessment.”

The rebels are seeking both closer ties with the EU on issues like trade and customs, and to ensure that the government does not follow through on its threat to leave the bloc without a deal if it does not like the terms on offer from Brussels.

Failure to appease the rebels would likely see May defeated in parliament in the coming weeks, blowing apart Tuesday’s hard-won truce and badly undermining her leadership of a minority government and a divided political party.

The government said it would produce its revised plan on Thursday. It will then be discussed in the upper chamber of parliament on June 18, before returning to the elected lower house for approval at an as-yet unspecified date in the near future.