Britain’s most senior official in charge of negotiating the country’s exit from the European Union has resigned because he was unwilling to be “a reluctant conscript” to Prime Minister Theresa May’s plans to leave the European Union, delivering a blow to a British leader struggling to end divisions among her ministers.

The late-night resignation of David Davis on Sunday is being praised by Brexit campaigners in May’s Conservative Party, who felt her plan to press for the closest possible trading ties with the EU had betrayed their desire for a clean break with the bloc.

His resignation seemed to spur others to follow suit, with a source saying that Steve Baker, a junior minister in the same department had also quit, just two days after May had held a crisis meeting with ministers to overcome the deep divisions over Brexit.

With nine months before Britain leaves and just over three before the EU says it wants a deal, May has been under intense pressure from the bloc and from many businesses to show her negotiating position.

Theresa May will face down a backbench revolt later this week as she fights for a soft Brexit. Photo: AAP

She thought she had done enough to move on with that fraught process at the meeting at her Chequers country residence. The resignations further complicate that process, and put a question mark over whether she can get the backing of parliament for her Brexit plans and whether there may be a leadership contest.

“The general direction of policy will leave us in at best a weak negotiating position, and possibly an inescapable one,” Davis said in his resignation letter to May.

He criticised May’s decision to maintain a “common rule book” with the EU, mirroring the bloc’s rules and regulations, saying it would hand “control of large swathes of our economy to the EU and is certainly not returning control of our laws”.

“It seems to me that the national interest requires a Secretary of State in my Department that is an enthusiastic believer in your approach, and not merely a reluctant conscript.”

May replied to his letter to say she did not agree “with your characterisation of the policy we agreed at cabinet on Friday”. She thanked him for his work.

Another minister from the Brexit department, Suella Braverman, was also reported by local media to have resigned.

After the hours-long meeting at Chequers, May seemed to have persuaded the most vocal Brexit campaigners in the cabinet, including Davis, to back her plan to press for “a free trade area for goods” with the EU and maintain close trade ties.

May’s environment minister Michael Gove said on Sunday that while the agreed negotiating stance was not perfect, he believed it delivered on handing back control to Britain.

-with AAP