Video report by ITV News Political Correspondent Emily Morgan.
Leading Brexiteer Jacob Rees-Mogg has attacked the Chancellor for backing a soft exit from the EU even as senior members of the Government attempted to heal a growing rift within the Conservatives over the issue.
He told Peston on Sunday that Philip Hammond's suggestion that UK relations with the EU would change only "very modestly" after Brexit had caused "real trouble" for the Government - and were at odds with what Theresa May had previously pledged.
"I tend to disagree with the Chancellor on many things but on this issue he seems to be disagreeing with Government policy, the Conservative party's manifesto and Mrs May's speeches," he said.
"This is real trouble for the Government. The history of chancellors being in opposition to prime ministers is not a good one or an encouraging one."
Asked whether he agreed with some pro-leave MPs that Mr Hammond should be fired, he said it was not him to direct the Prime Minister.
"Of course I've got a view, but I think it's not for me to give that view publicly. I think this really is a matter for the Prime Minister," he said.
"I'm being as loyal as I could possibly be on the policy question and I am biting my tongue on the personality question."
Mr Rees-Mogg said he backed Mrs May to remain as leader, and he was confident that she would "back her own policy" but returning to the cliff-edge exit she had promised in her Lancaster House speech.
His intervention comes amid growing discontent from pro-Brexit members of the party.
Many are calling for Mr Hammond's sacking after the Chancellor - a leading proponent of a soft Brexit - insisted that relations with the bloc would change only "very modestly"after the exit.
Backbench Brexiteer Nadine Dorries also called for Mr Hammond's head on Peston on Sunday.
"He has to go," she said, "The Chancellor needs to be singing off the Lancaster House hymn sheet along with the Prime Minister, he needs to have the Prime Minister's back and he doesn't."
Former cabinet minister Iain Duncan Smith told the Sunday Express: "The Prime Minister cannot govern with Philip Hammond sniping from the sidelines. She has got a serious negotiation on and she does not need the Chancellor contradicting government policy. She needs to say to him: 'You do that again and it will be your last comment as a cabinet minister'."
Senior members of the Government attempted to reassure pro-Brexit members of the party and soothe over rifts.
David Lidington, Mrs May's deputy, assured pro-Brexiteers that Mr Hammond is "fully on board" with the Government's Brexit strategy.
He today also insisted that the UK will "have the option" to diverge from EU rules during a post-Brexit transition period.