Remainers Amber Rudd, Damian Green and Justine Greening held a private meeting with Theresa May in which they claimed the majority of Tories favour a compromise with the EU.
The trio are reported to have asked the Prime Minister to ignore protests on extremes of the Party and pursue a policy which keeps the UK closely aligned to the single market and customs union.
Former Home Secretary Amber Rudd said: “That’s where the vast majority of the party is.
“We just haven’t been as shouty. We wanted to tell the Prime Minister what lots of MPs are telling us: sensible Brexit please.”
The move follows a series of informal consultations with backbenchers on both sides of the Brexit debate to build what the three ex-Cabinet members call a “pragmatic approach” to the negotiations.
But Ms Rudd ruled out remaining in the customs union, saying: “Whatever customs union alternative we go for we have to give ourselves sufficient time to deliver it.
“What is practical must be the guiding principle while protecting the Good Friday agreement.”
The three ministers are concerned the public debate on Brexit has been dominated by hardline Brexiteers and Remainers.
Former Education Secretary Ms Greening is understood to have had cups of tea with Brexiteers in a bid to persuade them to alter their position and agree to a compromise which would preserve Mrs May’s red lines of leaving the customs union and single market.
One Conservative MP said: “Justine has been having endless cups of tea with the Brexiteers trying to broker a compromise.
“All three of them have the advantage of having been in Government until recently and they understand the complexities of what the Government is trying to do.
“The more voices arguing for compromise the better.”
But one Remainer Conservative MP said they did not think the former Cabinet Ministers would be able to find common ground with Brexiteer backbenchers such as the former Cabinet Minister John Redwood.
They said: “I think some on that side of the party don’t want any kind of deal at all and will vote against whatever the Prime Minister comes back with.”
Downing Street has tried to play down the significance of the meeting.
They added Mrs May meets regularly with all sections of the Parliamentary Party and the meeting had been arranged “some time ago”.
Under the three former Cabinet Minister’s proposals, the UK would legally commit to remaining aligned with single market rules on goods in order preserve trade.
They also want the Government to pledge to stay in a customs union for a limited time while new arrangements are made to avoid disruption.