Mr Davis shocked the Prime Minister by telling her he could not support the Brexit plan agreed at Chequers on Friday, prompting speculation that a wave of Cabinet resignations could follow.
Conservative MP Peter Bone hailed Mr Davis' resignation as a "principled and courageous decision", adding: "The PM's proposals for a Brexit in name only are not acceptable".
UK Brexit Secretary David Davis has resigned, along with two other Brexit ministers.
Andrea Jenkyns said Mr Davis's departure was "fantastic news" and hailed Mr Baker as "another courageous and principled MP".
"The PM's proposals for a Brexit in name only are not acceptable", he said.
David Davis penned a deliberately caustic resignation letter last night outlining a "significant number" of disagreements with Number 10 over the past year, 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", Davis said in his resignation letter to May.
He was well acquainted with the Brussels beat: he was Europe minister between 1994 and 1997 as the European issue tore apart then Conservative prime minister John Major's government.
The UK is set to leave the European Union at the end of March 2019 and negotiators are under pressure to secure a deal by this autumn, in order for it to be ratified in time.
May was expected to tell MPs that the strategy agreed on at Chequers is the "right Brexit" for Britain.
Mr Jackson, who served as a city MP between 2005 and 2017, was chief of staff to David Davis who quit last night due to Britain's Brexit negotiating stance which he said was making it look "less and less likely" that the Conservatives would deliver their manifesto commitment to "leave the Customs Union and the Single Market".
While May's plan for exiting the European Union has not been fully revealed to all members of her party - let alone to Parliament, the business community or the public - the brief outline that was released shows she supports a middle way of compromise with Brussels, keeping Britain closely aligned with Europe on standards, "a common rule book for industrial goods and agricultural products".
Speculation is mounting that others, including Foreign Secretary Boris Johnson, are ready to quit.
An analysis of the Chequers deal circulating within the pro-Brexit European Research Group of MPs was damning about the plan, saying it would lead to "a worst-of-all-worlds "black hole" Brexit where the United Kingdom is stuck permanently as a vassal state in the EU's legal and regulatory tar pit". Environment Secretary Michael Gove said Sunday that it did not contain everything he wanted but "I'm a realist".
Over the weekend May sought to bind Brexit supporting ministers to her proposal as they were sent out to tell the media that they backed it.
The Prime Minister will insist the plan, which would see the UK share a "common rulebook" for goods as part of a proposal to create a UK-EU free trade area, still meets her Brexit red lines.