The Gravesham MP Adam Holloway has joined those calling for a vote of no confidence in the leadership of Theresa May.
The MP submitted a letter asking formally requesting a vote.
He has insisted that his decision does not reflect a personal criticism of the PM but believes the deal that has been struck is not one that he can support.
On his Facebook page the MP wrote: "My letter of No Confidence has now been delivered - with regret. Mrs May is a remarkable woman - just look at her fortitude today in the House of Commons, even more please remember her long career of public service.
"But as we see from the events of today, you can not have someone leading a mission who does not believe in the mission. The country needs Leadership."
He is thought to be the first county MP to declare his hand. Gravesham county councillor Bryan Sweetland said: “ I am not surprised by this. It is nothing personal against the prime minister but he has always been a strong supporter of Brexit and Gravesham was one of the areas that strongly supported leaving the EU in the referendum.”
It is understood that Mr Holloway spoke with constituency officials last night before submitting his letter explaining his reasons.
Meanwhile the business Secretary and Tunbridge Wells MP Greg Clark has come out to back Theresa May's Brexit deal.
Under party rules it would require 48 MPs to submit letters asking for a vote of no confidence to trigger a leadership contest.
Mrs May endured a torrid day yesterday but ended it by coming out fighting and saying that she intended to stay on and push the deal through.
It's understood all government whips have been told to cancel any engagements today and return to London.
Sky News sources says a no confidence vote in Theresa May is now "likely" as there's growing upset over her draft Brexit plan.