"You deserve the final say on this shambolic Brexit with the chance to stay in the European Union".
"The government now has a song to sing", he said. His role as Brexit Secretary was crucial to ensuring Britain leaves the European Union next year with what Mrs May described as the "best possible deal".
Many people now see a General Election as an increasingly likely result of these resignations, but that would need a leadership challenge before that. "There was always going to be a moment in time that was needed for the British Prime Minister to show her authority because she had a very divided cabinet on her approach to Brexit", he said.
Britain has given up trying to keep full access to the European Union market for its giant financial services sector after Brexit and instead will push for an easing of existing rules, the Financial Times reported.
The plan agreed at May s country retreat at Chequers near London last Friday would involve Britain pursuing a "UK-EU free trade area" for goods that would involve regulatory alignment with the EU.
He told the Today programme: "If the Prime Minister thinks she has consent and support from every member of her Cabinet she is deluding herself, as we have just seen".
Britain's Prime Minister Theresa May leaves Downing Street in London, Britain, July 10, 2018.
'The Chequers deal is a plan that has been put together, it's been agreed by government, ' she said as she arrived in Brussels for the North Atlantic Treaty Organisation summit.
This has angered some Conservative backbenchers, who say it will prevent the United Kingdom from having its own independent trade policy, and they want to see the Chequers blueprint rewritten. Pro-Europeans want to retain close economic ties with the bloc and its market of 500 million people, while some, but not all, Brexit supporters want a clean break to make it possible to strike new trade deals around the world.
Why did David Davis resign?
The two resignations have left May badly exposed and raised questions over whether she will stand firm in her commitment to pursuing a "business-friendly" Brexit, or will be faced with more resignations and calls to quit herself.
The Daily Telegraph said on Tuesday night that senior Brexiteers said that they have enough letters in hand to trigger a confidence vote and will submit them unless she hardens her Brexit plans.
But striking a beneficial trade deal with the United States was always going to be hard for the United Kingdom, which will lack the negotiating power enjoyed by the European Union.
The truce did not last the weekend after Davis quit on Sunday night, warning that Britain was "giving too much away too easily" in Brexit talks.
But many eurosceptic MPs are outraged at May's plan, and Davis's resignation letter was scathing.
Earlier staunch Brexiteer Dominic Raab was named as Mr Davis's replacement as Secretary of State for Leaving the EU.
While May is certainly in a precarious situation, the absence of banner-barer leading the charge for a clear and widely supported alternative position to the Chequers deal makes her relatively safe for now. "It's not even an accidental betrayal, it was planned and plotted well in advance", said Conservative lawmaker Andrew Bridgen.
"But I come back to this point, if people don't like this proposal what is their alternative?"