Davis's late-night resignation undermines May's fragile government.
The FTSE .FTSE was up 0.15 percent by 0841 GMT, joining a bounce in global equity markets, which continued to benefit from Friday's strong U.S.jobs report.
British Prime Minister Theresa May pledged on Monday to pursue a newly agreed strategy to quit the European Union, in a challenge to those who may want to follow her former Brexit minister and quit in protest at what he called her "dangerous" plans.
During a 12-hour meeting on Friday, May's fractious cabinet - including Davis - finally agreed on a plan for future trade ties with the EU.
"The PM said in her letter to the secretary of state that she didn't agree with his characterization of the position".
Some Brexit-supporting lawmakers are angry at the proposals, saying they will keep Britain tethered to the bloc and unable to change its rules to strike new trade deals around the world.
She said the government's Brexit plan was "far from perfect" but marked "grown-up steps". Davis and Baker, both longstanding eurosceptics, decided they could not support the policy, a person familiar with the matter said.
Mr Davis was appointed Brexit secretary in 2016 and was responsible for negotiating the United Kingdom withdrawal from the EU.
"Well done David Davis for having the principal and guts to resign".
In a letter responding to Davis' resignation, she said she was "sorry" he had chosen to resign and argued her proposal was "consistent with the mandate of the referendum". But some senior pro-Brexit ministers have backed May's plan.
May's plan would create a free trade area with the European Union for goods, to protect supply chains in areas such as manufacturing, while maintaining flexibility for Britain's dominant service sector.
"A very soft Brexit means that we haven't left, we are simply a rule-taker", he said.
It won the backing of one other prominent Brexit campaigner. Environment Secretary Michael Gove said Sunday that it did not contain everything he wanted but "I'm a realist".
He told BBC 5 Live: "These proposals will have to come to the House of Commons in legislation and the question is 'will they command support from Conservative MPs?'".
"I would like to thank you warmly for everything you have done over the past two years as Secretary of State to shape our departure from the European Union", she said.
- His departure leaves May with a hard task to find a replacement who can win the confidence of the pro-Brexit faction in May's Conservative Party whilst delivering on a Brexit plan that outraged many of them.
Jacob Rees-Mogg, the leader of a Conservative group of Brexit supporters, said Davis' resignation proved that their concerns were well-founded and signaled that he would not vote for May's plan if it came to a vote in parliament.
Tory Andrew Bridgen said he could not support the proposals that came out of Chequers, describing them as a breach of the red lines and that he wouldn't support it "even if the European Union were paying us for it".
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