Shipley MP Philip Davies said he had been contacted by members and voters in his constituency about the Prime Minister's Chequers plan for a "common rulebook" with the EU on goods and agri-goods, and it was "clear that many people are concerned by this".
In a letter to his constituents, Mr Davies said the Chequers plan on trade is "unacceptable" and revealed he was concerned that proposals to give EU citizens preferential immigration status for work and study "will go too far".
It comes after Mrs May survived a series of knife-edge Commons votes which had the potential to sink her fragile premiership.
The PM also received a boost at a meeting of the backbench 1922 Committee on Wednesday night when Eurosceptic MP Simon Clarke said he had changed his mind about trying to topple her.
Mr Clarke said he had withdrawn a letter calling for a confidence vote in Mrs May because Brexit had taken the Tory party to "breaking point", stating: "We have looked into the abyss in the last few days."
But Mr Davies' letter at least cancels out Mr Clarke's withdrawal.
The Shipley MP wrote: "Politics is all about trust and once it is lost it is impossible to win back. Many people have told me that as a result of this they have lost trust in the PM to properly and fully deliver the referendum result. It is with much sadness that I have to say that I have also lost trust in her to deliver the referendum result too.
"Failure to keep our promise to the electorate will almost certainly lead to the catastrophe of Jeremy Corbyn becoming Prime Minister and I cannot sit back and allow that to happen.
"Therefore I have reluctantly come to the conclusion that I have no alternative but to send a letter to the Chairman of the 1922 Committee asking him for a vote of no confidence in the Prime Minister. If 48 such letters are sent a vote of no confidence in the Prime Minister amongst Conservative MPs will take place.
"This is a secret process and people do not need to declare that they have sent such a letter, but I believe you (and my constituents) have the right to know what I do as your local MP and that is why I am writing to let you know. Some of you will agree with my decision and some of you will disagree - I am well aware of that. But you all have a right to know.
"I always have to look you all in the eye and tell you that I have done what I believe is right for the country and our Party. This has not been an easy decision and I have agonised over it, but I know in my heart of hearts it is the right decision.
"I hope that the Conservative Party and I can look forward to your continued support at what I appreciate is a very difficult time."
Responding to Mr Davies' letter, Liberal Democrat Brexit spokesman Tom Brake said: “The Tories are only now willing to accept that they have lost trust in Theresa May, but the public lost trust in her a long time ago. The end is near for May.
“The Tories cannot agree a negotiating stance on Brexit, never mind strike a deal with the EU. This Government is a complete and utter shambles, and even their own backbenchers know it.
“Given the chaos, now more than ever people deserve a final say on the Brexit deal and an opportunity to exit from Brexit.”