Mr Lidington has been working with Ireland’s Taoiseach Leo Varadkar and Foreign Minister Simon Coveney in the final stages of Brexit negotiations between the UK and EU.
But Mr Raab accused Mr Lidington of “going behind his back”, according to the Brexit Secretary’s allies.
One senior Conservative told the Sun: “Dominic is furious. He feels he is being undermined at every turn.
“The Government is being run by Philip Hammond, Greg Clark and David Lidington. And they all want to stay in the customs union.”
It is the latest row that threatens to further split Brexiteers and Remain MPs in Mrs May’s divided party.
The clash comes as tensions are running high over the issue of the Irish border as the UK battles to strike a Brexit deal with the EU.
The Prime Minister is pushing for a UK-wide backstop, which would keep the whole of the UK in the customs union if no trade deal is made with the EU by the end of the transition period in December 2020.
But a leaked letter from Mrs May to DUP leader Arlene Foster revealed the EU’s demands for a Northern Ireland-only backstop if the UK-wide arrangement breaks down, meaning a border in the Irish Sea.
In the letter, Mrs May said: “I am clear that I could not accept there being any circumstances or conditions in which that ‘backstop to the backstop’, which would break up the UK customs territory, could come in to force.”
But the DUP, which the Prime Minister relies on for her majority in the House of Commons, rejected the proposal.
DUP leader Arlene Foster said: “The Prime Minister’s letter raises alarm bells for those who value the integrity of our precious union and for those who want a proper Brexit for the whole of the UK.
“It appears the Prime Minister is wedded to the idea of a border down the Irish Sea with Northern Ireland in the EU single market regulatory regime.”
Culture Secretary Jeremy Wright denied the Government would accept a Brexit deal which splits up the UK.
Speaking to BBC Radio 4, Mr Wright said: “Were there to be a border down the Irish Sea, as I’ve said and the Prime Minister has said, we wouldn’t accept a deal incorporating that.”