Robert Courts left his role as a ministerial aide saying he could not look himself in the mirror if he had been forced to defend the prime minister’s plans.
The MP, who now sits in David Cameron’s old seat, indicated he would vote against the government in a house of commons vote on Monday.
The resignation follows those of David Davis, Boris Johnson and Steve Baker last week, with more suspected in anger over the proposals set out in Ms May’s latest Brexit white paper.
Announcing his resignation on Twitter, Witney and West Oxfordshire MP Mr Courts said: “I have taken very difficult decision to resign position as [parliamentary private secretary] to express discontent with the Chequers [plans] in votes tomorrow.
“I had to think who I wanted to see in the mirror for the rest of my life. I cannot tell the people of WOxon that I support the proposals in their current form.”
The prime minister is trying to push through two bills this week, with Brexiteer rebels placing wrecking amendments on them.
Labour has said it will not support the amendments making it unlikely they will go through, but it could give the Brexiteers an opportunity to show their strength.
Ms May appealed to warring Tory MPs to back her blueprint for Brexit and avoid a disorderly withdrawal from the EU which she said would damage Britain’s interests.
The prime minister said she had been forced to come forward with the revised proposals after the EU had offered two options, neither of which was acceptable.
She explained: “Faced with that we had an option. We could go for no deal, no deal is still there, it is still possible, but I think the best thing for the UK is to have deal that sets a good relationship with our trading partners in the future.
“So if we were going to find something that was Britain’s interest, that delivered on the referendum and that was negotiable, we had to make what is a compromise but is a positive in terms of the benefits it gives us.”
Ahead of a crucial week in Parliament, the Prime Minister acknowledged feelings in the party were running high, but said her plan offered a “hard-headed and practical” way forward.
However leading Brexiteer Jacob Rees-Mogg warned trust in Ms May was waning amid acrimonious claims key ministers, including Mr Davis, were kept in the dark about her proposals.
In a scathing aside, he accused her of failing to embrace the opportunities of Brexit, saying she was “a Remainer who remained a Remainer”.
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