In a statement posted on Twitter, he said: “We are a proud nation and it is a say day when we are reduced to obeying rules made by other countries who have shown that they do not have our best interests at heart.”
He added: “We can and must do better than this. The people of the UK deserve better.”
Also on Twitter, DUP MP Sammy Wilson said Mr Vara was “a man of his word”.
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Mr Vara’s resignation came as European Council president Donald Tusk announced an extraordinary meeting of EU leaders in Brussels on November 25, at which the withdrawal agreement and a political declaration on future relations will be finalised and formalised.
Mr Vara’s departure comes 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.
Westminster was 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.
The Prime Minister cleared the first hurdle when Cabinet ministers finally approved the draft terms of her agreement with Brussels at a stormy five-hour meeting on Wednesday.
But she now faces a battle to get it through Parliament as pro-Leave Conservative MPs - as well as some Remainers - lined up to condemn the plan, accusing her of breaking promises and leaving the UK at the mercy of Brussels.
In a resignation statement, North-West Cambridgeshire MP Mr Vara - who was promoted by Mrs May as recently as July - said: “We are a proud nation and it is a say day when we are reduced to obeying rules made by other countries who have shown that they do not have our best interests at heart.”
Meanwhile, Shadow Brexit secretary Sir Keir Starmer has told Good Morning Britain the deal was a “miserable failure of negotiation” and it was a “second-rate document”.
He told the ITV programme: “It’s a chaotic ending and the root cause is the utter division on the Conservative benches.”
MPs should back Theresa May’s Brexit plan because the alternatives to it are “ugly”, Health Secretary Matt Hancock said.
He warned that failing to get the deal agreed with Brussels through Parliament would either lead to a no-deal Brexit or a second referendum and the risk of not leaving at all.
He told BBC News: “All MPs should vote for it because this deal is in the national interest.
“The two alternatives are deeply unattractive and as people read the detail of it and look at the deal in the round, rather than the bits and pieces that have come out in the newspapers during the latter stages of the negotiations, anybody in any compromise negotiated document can pick out individual parts that they would prefer were written differently.”
European Council president Donald Tusk has set out the process leading up to a Brussels summit of EU leaders on November 25 at which the UK’s withdrawal agreement will be finalised and formalised.
At a press conference in Brussels, Mr Tusk was presented by the EU’s chief negotiator Michel Barnier with a copy of the 585-page agreement approved on Wednesday by Theresa May’s Cabinet.
Mr Tusk said that the agreement was already being analysed by all the member states, and by the end of this week the EU27 ambassadors will meet in order to share their assessment.
“I hope that there will not be too many comments,” he said.
Ambassadors and ministers of the EU27 will also discuss the mandate for the European Commission to finalise the joint political declaration on future UK/EU relations published in outline form on Wednesday with the intention of agreeing a final form of the declaration by next Tuesday.
Over the following 48 hours, member states will evaluate the document and sherpas should conclude the work on November 22, allowing the European Council to convene at 9.30am on November 25 “if nothing extraordinary happens”.
Welcoming the approval of the draft agreement by Theresa May’s Cabinet, Mr Tusk said: “Of course, I do not share the Prime Minister’s enthusiasm about Brexit as such.
“Since the very beginning, we have had no doubt that Brexit is a lose-lose situation and our negotiations are only about damage control.”
Thanking Mr Barnier for his work as chief negotiator, Mr Tusk said: “You have achieved our two most important objectives: You ensured the limitation of the damage caused by Brexit and you secured the vital interests and principles of the 27 member states and of the European Union as a whole.”
In a message to the British people, Mr Tusk said: “As much as I am sad to see you leave, I will do everything to make this farewell the least painful possible, both for you and for us.”