Brexit Secretary David Davis has resigned because he was not willing 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 was 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 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.

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 criticized 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.

In another blow, a government source said that Steve Baker, a minister who worked for Davis and who while in government gave many Brexit campaigners faith in the process, had also resigned.

Another minister who works alongside them could also follow them to the door, party sources said.