He said it looked less and less likely the party would deliver on the Brexit result and the Tory commitment to leave the customs union and single market.
The general direction of policy will leave us in at best a weak negotiating position, and possibly an inescapable one, Mr Davis writes in his resignation letter.
It comes as Theresa May contends with a backlash against the new plans for Britain’s future relationship with the European Union.
Pro-Brexit Tories are angry about the plan, with speculation it could end up in a leadership challenge.
Analysis – PM must fight for job after ‘remarkable’ resignation
Mr Davis’s junior ministers, Steve Baker and Suella Braverman, have also resigned.
The cabinet – including Mr Davis – all signed up to the proposals after a meeting at Chequers last week.
But in his letter he attacks the plans, saying they will make the supposed control by Parliament illusory rather than real.
I am also unpersuaded that our negotiating approach will not just lead to further demands for concession, he tells the prime minister.
He ends by saying that Mrs May needs an enthusiastic believer in your approach, and not merely a reluctant conscript.
In full David Davis resignation letter and Theresa May’s response
Who could replace David Davis as Brexit secretary?
Here is David Davis resignation letter pic.twitter.com/Qzj2rLaw6z
The PM is due to set out the Brexit plans in parliament later, before a potentially stormy meeting with her own MPs.
In her own letter, Mrs May thanks Mr Davis for his service, but tells him I do not agree with your characterisation of the policy we agreed at Cabinet on Friday.
Hitting back at his claims, the prime minister sets out 12 points how we will deliver on the result of the referendum and the commitments we made in our manifesto.
They include ending free movement, a new business-friendly customs model, no more sending vast sums of money each year to the EU, and no hard border between Northern Ireland and Ireland.
The PM adds At Chequers on Friday, we as the Cabinet agreed a comprehensive and detailed proposal which provides a precise, responsible, and credible basis for progressing our negotiations towards a new relationship between the UK and the EU after we leave in March.
What exactly is May’s new Brexit plan?
Sky’s political correspondent Lewis Goodall called Mr Davis’s resignation an absolute bombshell.
He said To resign tonight after the emergency meeting at Chequers on Friday is really quite shocking when you consider, apparently according to the briefing we received, that every single member of the cabinet – admittedly some with their reservations – all agreed that they would support the prime minister’s proposals and they would defend them in public.
The big question now is, is David Davis going to be joined by any other figures? All eyes of course will be on Boris Johnson and other Brexiteers.
Foreign Secretary Boris Johnson reportedly described defending the Brexit plans as like polishing a turd during the Chequers summit, before eventually falling into line behind the prime minister.
Jacob Rees Mogg tells me This is very important. It raises the most serious questions about the PM’s ideas. If the Brexit Secretary cannot support them they cannot be very good proposals. It was an attempt to bounce the cabinet. It was a seriously mistake.
He adds, It is not her finest night in politics.
Leading Brexiteer Jacob Rees-Mogg told Sky’s Lewis Goodall This is very important. It raises the most serious questions about the PM’s ideas.
If the Brexit Secretary cannot support them they cannot be very good proposals. It was an attempt to bounce the cabinet. It was a serious mistake.
He added It is not her [Theresa May’s] finest night in politics.
A leadership contest would be triggered if 48 Conservative MPs formally submit letters, and some have already reportedly been sent to the Tories’ backbench 1922 Committee.
The prime minister said on Friday that the proposals were good for the UK and good for the EU and would deliver prosperity and security.
They include the creation of a UK-EU free-trade area, so that Britain would have the same rules for all goods as it currently does as a member of the European Union.
In her appearance in the Commons later, Mrs May will admit the cabinet have had robust views but will insist she has listened to every possible idea and that this is the right Brexit.
She will tell MPs the proposals will deliver on the democratic decision of the British people.
Environment Secretary Michael Gove – a key figure in the 2016 Leave campaign – said on Sunday that the plans were not everything he had hoped for, but that he was a realist.
He called them a perfect balance between the need for close access to Europe and allowing the services industry to diverge from EU rules and regulations.
EU leaders have warned time is running out to get a Brexit deal sorted. The UK is due to leave on 29 March next year.
News Source SkyNews