The resignation comes two days after the whole of the cabinet met at Chequers to agree Britain's negotiating position.
Conservative MP David Davis arrives at Downing Street on July 13, 2016 in London, England.
In his resignation letter, Mr Davis said he could no longer be an "reluctant conscript" to the Prime Minister's strategy on leaving the EU.
"The PM's proposals for a Brexit in name only are not acceptable".
Ian Lavery, chair of the Labour Party, said: "This is absolute chaos and Theresa May has no authority left".
David Davis penned a deliberately caustic resignation letter last night outlining a "significant number" of disagreements with Number 10 over the a year ago, from being obliged to accept the Brussels sequencing of negotiations, through to the compromises on the Northern Ireland border last December.
"The general direction of policy will leave us in at best a weak negotiating position and possibly an inescapable one".
Yet after reflecting on the situation, Mr Davis and Mr Baker apparently decided they could not live with such a soft Brexit after all.
Japan says death toll from floods climbs to 100 The Okayama prefecture said three people had died, six others were missing and seven were injured, while almost 500 were flooded. At least 60 people have died in Japan as the country is battered by the worst rains and flooding in the country's history.
Syrian rebels lose string of southwest towns Israeli officials said they can't possibly take in 160,000 refugees, but are trying to do everything possible to help them. Forces loyal to Syria's President Bashar al-Assad are deployed in al-Ghariya al-Gharbiya in Deraa province.
Trump spoke with three Supreme Court candidates Possible nominees being eyed include Thomas Hardiman, who serves alongside Trump's sister on the Philadelphia-based 3rd U.S. Eager to build suspense, Trump wouldn't divulge whom he's talking to in advance of his big announcement, set for July 9.
An opinion poll found that 35 per cent believe the Brexit compromise agreed by the Cabinet is the best deal Britain will get from the European Union, while 38 per cent dismissed it as a sell-out.
The resignations of Davis and Baker came just two days after the premier announced she had secured the backing of her cabinet for a plan to keep close ties to the European Union after leaving the bloc.
Junior minister Steve Baker quit shortly after Mr Davis - as Mrs May prepares to face MPs and peers later.
"And I think without David Davis there, without his imprimatur, it will be very hard for them to get the support of Conservative MPs and therefore the prime minister would be well advised to reconsider them".
May is due to brief lawmakers Monday on the plan hammered out during a 12-hour meeting at Chequers, the prime minister's country retreat.
In that meeting, May had appeared to win over her fractious cabinet and secure approval for her plan, which was to be published as soon as this week in a lengthy white paper that would stake out Britain's vision for future relations with Europe. Michael Gove, May's environment minister, said on Sunday that while the agreed negotiating stance was not flawless, he believed it delivered on handing back control to Britain.
Allies made it clear that the foreign secretary has not chosen to publicly support the Chequers deal yet - unlike Environment Secretary Michael Gove, Commons Leader Andrea Leadsom, and Trade Secretary Liam Fox.
Jacob Rees-Mogg, chair of the European Research Group of Tory Europsceptic MPs was being urged to run for leader, with one even naming him as "our Churchill".
They accuse May of backtracking on her professed red lines in the negotiations.
Boris Johnson, a leading critic of the plans, spent several minutes at the Chequers summit spelling out his concerns, saying anybody defending the deal would be "polishing a turd" if they tried then to sell it to the party and the public.
Tehran dismissed it is an orchestrated "false flag ploy", created to discredit Iran and overshadow Rouhani's trip to Europe. Iranians have complained that the hoped-for rise in foreign investment and trade after the deal has not materialised.
Initial euphoria over finding the boys alive quickly turned into deep anxiety as rescuers struggled to find a way to get them out. The boys and their coach had been stranded in Tham Luang Nang Non when they went exploring in the cave after a scrimmage June 23.
Two people on the boat were not injured, passengers from a neighboring boat captured the aftermath of the explosion on video. He said his niece remains in critical condition in a medically induced coma at a Nassau hospital.
The trade dispute between the United States and China escalated on Friday, but Wall Street focused on a solid jobs report instead. Importers of American retail goods hit by higher Chinese duties were reluctant to pass the costs on to consumers for now.
Selena didn't think they were even that serious, so the thought of them getting married is just mind-boggling to her. His mother, Pattie Mallette , tweeted " Love Love Love Love Love Love Love ." on the same night of the engagement .
But both Canadian and American fishermen said they noticed increased activity in harbors and in the Atlantic in early June. The State Department did not respond to a request for comment. "Absolutely overkill", he said of the "disturbing" stops.
Video from Thai Navy special forces on Monday showed the boys looking emaciated but smiling and at times laughing . The magnitude of the problem has now overtaken the initial rejoicing when they were found earlier this week.
Reliance Industries Chairman Mukesh Ambani said that the FTTH service will be provided in 1,100 cities across the country. It now offers fibre-to-the-home (FTTH) broadband connections with 1.1TB (terabytes) of free data at a speed of 100 mbps.
A tropical storm warning remained in effect for Dominica and Guadeloupe, while a tropical storm watch was issued for Barbados, St. We'll continue to monitor this feature and provide updates during NBC2 Newscasts throughout the next several days.
The most obvious name thus far hasn't been a free agent, but a guy under contract and unhappy with the San Antonio Spurs . The Lakers could've been pressured to overpay in Leonard traded if they felt it would have landed the four-time MVP.
Unless Ball is traded away, he would most likely be demoted to a bench role with fellow youngsters Josh Hart and Moe Wagner. His stats as a starter: 18.6 points, 9.1 rebounds, 3.1 assists on 56.0 percent shooting in 29.9 minutes per game.
Trump says OPEC is 'doing little' to lower gas prices
However, the Chinese government has not yet specified a date on which it may introduce duties on imports of US crude. Even so, renewed US sanctions on Iran against its oil exports look set to tighten supply further.
England wins first ever World Cup shootout to reach quarters
And asked whether England can start dreaming of glory if they beat Colombia , Rooney said: "I think we should be dreaming now". David Ospina will play a grander role in calming the defensive line and ensuring they keep their shape and cool on the pitch.
Amazon Prime Day 2018 announced with big deals
Amazon promises an additional 10 percent off hundreds of sale items at Whole Foods and deeper discounts on some popular products. This will be the first Prime Day with Whole Foods Market under the Amazon umbrella, and the grocer will be front and center.
Google lets 3rd-party app developers read your emails
Company computers, which scan some 100 million emails a day, were "trained" by workers who personally read thousands of emails. You may need to research each individual program or service to make an educated decision.