The Chancellor provoked fury among hardcore Brexiteers in his own party this week after saying Britain would only change “very modestly” when it leaves the bloc.
Those words earned him a rebuke from Downing Street but risked inflaming tensions further yesterday by saying the UK should seek a “middle way” in Brexit negotiations in order to maximise access to EU markets.
Mr Paterson hit out at the Chancellor last night, saying: “If he goes on like this, publicly flouting her, I think she might have to sack him.
“There is a perfectly simple option for Cabinet ministers who do not want to adhere to Government policy – resign and go to the back benches.
“This is all very unhelpful, because Michel Barnier must be watching and thinking ‘what does Britain actually want?’
“This all looks like a Project Fear campaign by Remainers but most Tories just want to get on with Brexit and get it done.”
Brexit Secretary David Davis was forced yesterday to play down mounting disquiet among Tory backbenchers over Theresa May’s leadership.
Mr Davis insisted there was “no difference” between himself, the Chancellor and the PM on the outcome they were seeking.
In an apparent attempt to show unity on Friday evening, Mr Davis, Mr Hammond and Business Secretary Greg Clark wrote an open letter to reassure business leaders the UK would maintain continuity with EU rules during transition.
But Jacob Rees-Mogg warned the Government against delivering “Brino” – Brexit in name only.
He said: “The less of Brexit you get, the more likely you are to get Jeremy Corbyn.
“If you get a good, clean Brexit and get the advantages from it then the chances of getting Jeremy Corbyn are much diminished.
If everything is delayed for two years and then there’s high alignment, you will find that by 2022 no-one will have noticed any difference from having left.
“Then what will be the point of voting for the party that’s implemented it. I’m against ‘Brino’ (Brexit in name only).”
Mr Rees-Mogg insisted the PM has his “full support” and said Mr Hammond appeared to be “obstructing Brexit”.
But he added: “If the Conservative Party doesn’t deliver the Brexit that the British people voted for, the Conservatives will not win the next election. The leader is important, but the party is more important.
“Brexit is more important than anyone other than the Queen.”
Discontent among Tories has led to reports that the number of MPs who have written to Sir Graham Brady, the chairman of the backbench 1922 Committee, calling for a leadership contest is close to the trigger point needed to force a battle aimed at toppling Mrs May.