Brexit secretary Raab's resignation throws Mrs May's government into turmoil amid rumours more ministers could resign before the end of the day.
The pound fell heavily against most major currencies after Mr Raab's resignation – with the sterling dropping 1.1% to 1.28 US dollars and was 1.2% lower at 1.13 euros.
Raab's surprise departure came amid a furious backlash from Brexit-backing Tories to the deal agreed by UK and EU negotiators four months ahead of the UK's scheduled withdrawal on March 29.
Hours earlier Shailesh Vara had quit as minister of state for Northern Ireland, saying Mrs May's agreement, "leaves the UK in a halfway house with no time limit on when we will finally be a sovereign nation".
In his letter to the Prime Minister, Mr Raab said the deal represented a "very real threat to the integrity of the United Kingdom" because of provisions for Northern Ireland.
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“No democratic nation has ever signed up to be bound by such an extensive regime”
Dominic Raab
He also said he could not accept "an indefinite backstop arrangement" for the Irish border.
He said: "No democratic nation has ever signed up to be bound by such an extensive regime, imposed externally without any democratic control over the laws to be applied, nor the ability to decide to exit the arrangement."
He added: "Above all, I cannot reconcile the terms of the proposed deal with the promises we made to the country in our manifesto at the last election.
"This is, at its heart, a matter of public trust."
RESIGNED: Dominic Raab has quit as Brexit secretary in a major blow to Theresa May (Pic: GETTY)
The resignations came as European Council president Donald Tusk announced an extraordinary meeting of EU leaders in Brussels on November 25.
It is expected at this meeting the withdrawal agreement and a political declaration on future relations will be finalised and formalised.
Westminster is braced for further resignations, amid widespread expectations that the Prime Minister may face a challenge to her position from Conservative MPs submitting letters of no confidence in her leadership.
Backbenchers from the powerful European Research Group – chaired by Jacob Rees-Mogg – are expected to lead the charge against Mrs May.
PRIME MINISTER: Theresa May could face a challenge to her leadership before the end of the day (Pic: REUTERS)
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BRUSSELS: EU bosses Michel Barnier and Donald Tusk are optimistic over the deal (Pic: AFP)
Shadow Cabinet Office minister Jon Trickett said: "The Government is falling apart before our eyes as for a second time the Brexit Secretary has refused to back the Prime Minister's Brexit plan.
"This so-called deal has unravelled before our eyes.
"This is the 20th minister to resign from Theresa May's Government in her two-year premiership.
"Theresa May has no authority left and is clearly incapable of delivering a Brexit deal that commands even the support of her Cabinet – let alone Parliament and the people of our country."
STRUGGLING: Theresa May managed to push through her Brexit deal draft at Cabinet last night (Pic: REUTERS)
Remain-backing Conservative MP Anna Soubry tweeted: "Raab's resignation marks the end of PMs Withdrawal Agreement. This is very serious.
"The PM will clearly be considering her position. My own view is that we need a Govt of National Unity and we need it now."
Following the Brexit Secretary's resignation, former UKIP leader Nigel Farage tweeted: "Well done Dominic Raab, a few more and we will be rid of this duplicitous Prime Minister."
Cabinet ministers Esther Mcvey, Penny Mordaunt and Andrea Leadsom have all been named as potential resignees after Mrs May pushed her draft through last night.
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