London  - Former Brexit Secretary David Davis said Monday he had resigned because he felt British Prime Minister Theresa May is "giving too much away, too easily" in her latest Brexit proposals, though he backed her to continue as prime minister.

British media said the resignations of Davis and Steve Baker, a junior minister and prominent Brexit advocate, had plunged her government into a new crisis, one year after many analysts wrote off her long-term political leadership prospects.

"We are giving too much away, too easily"

The resignations were supported by many other "Brexiteers" in May's Conservative party, including influential right-winger Jacob Rees-Mogg, who leads some 60 lawmakers in the Conservative pro-Brexit European Research Group.

May moved swiftly to appoint pro-Leave Conservative lawmaker Dominic Raab as Davis' successor.

Davis told the BBC that he felt unable to promote a policy that he no longer believed in.

"It seems to me we are giving too much away, too easily, and that’s a dangerous strategy at this time," he told the broadcaster.

An EU spokesman said Davis' resignation would not be a problem for the European Commission, adding that the bloc will continue to negotiate with the British government in "goodwill" to reach a Brexit deal.

"We will continue to negotiate in goodwill, bona fide, with Prime Minister [Theresa] May and the UK government negotiators in order to reach a deal," said commission spokesman Margaritis Schinas.

Asked if Davis' resignation is a problem, he answered: "Not for us."

Asked in the BBC interview about a potential challenge to May's leadership of the party, Davis said it would be "the wrong thing to do," claiming that his resignation could even strengthen her position.

"She has got to have a Brexit secretary who will deliver on her strategy," he said. "That is not weakening, that is actually enhancing the effectiveness of the strategy."

May sorry for Davis' leave

Former lawyer Raab, 44, had been a junior housing minister since January and previously served in the Justice Ministry.

Rees-Mogg - tipped as a potential challenger to May - also said he did not expect May to face an immediate no-confidence vote, which would be sparked by the dissent following a marathon session of her cabinet to agree new Brexit proposals late Friday at Chequers, the prime minister's retreat outside London.

"No deal is better than a bad deal, and Chequers looks pretty poor," he tweeted.

"I think what the prime minister needs to do is give up on the Chequers proposals which, David Davis has pointed out in his resignation letter, don’t actually deliver Brexit," Rees-Mogg said on his radio programme for London broadcaster LBC.

In his resignation letter, Davis said he had been a "reluctant conscript" to May's Brexit policies, claiming they were making it "look less and less likely" that Britain will leave the EU customs union and single market, as May had promised.

In her reply to Davis, May said she disagreed with Davis' "characterization of the policy we agreed at cabinet on Friday."

"I am sorry that you have chosen to leave the government when we have already made so much progress towards delivering a smooth and successful Brexit, and when we are only eight months from the date set in law when the United Kingdom will leave the European Union," wrote May, who was scheduled to brief parliament on her new plan later Monday.

Davis is the sixth cabinet secretary to leave the government since an ill-fated snap election May called in June last year which left the Conservatives short of a majority and dependent on support from Northern Ireland's Democratic Unionist Party (DUP) for key votes in parliament.