Mr Baker said: “It is really important that the next Prime Minister is genuinely enthusiastic about the decision this country has taken.
“I am very confident that whoever wins, even Tom Tugendhat or Jeremy Hunt, they will follow the path that this country has now embarked upon – this relationship with the EU and indeed repairing the Northern Ireland protocol.
“But there is no substitute for genuine belief in what you are doing.”
He also recounted a story of how Ms Braverman had made him even look soft on Brexit during the Theresa May years when she was trying to push through the so-called Chequers compromise.
Both Baker and Braverman had quit as ministers in protest over Mrs May’s failure to take on the EU in the talks.
But with the third meaningful vote looming and the risk of Britain being dragged back into the EU, Mr Baker had a “wobble” and considered backing the deal along with the then ERG chairman Jacob Rees-Mogg.
Instead, Ms Braverman was one of the few “Brexit Spartans” who held out and stood firm ensuring Mrs May lost the vote and helped persuade him to oppose it too.
He said: “It is really important that Suella is Prime Minister because when even I wobbled, she was still firm and she was firm because she understood all the details and she knew she wasn’t willing to bend.
“I found somebody with even more resolve than me and I am not ashamed to admit that.”
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“I couldn’t possibly win that’s what emerged after I said I was seriously considering it.
If I could get to Conservative Party members, I might stand a really good chance and I am really honoured by what members have been saying to me and the messages of support I have had.
“But amongst MPs without cabinet experience, there is no chance.
“I am really pleased and proud to back Suella.
“She has the resolve, the authenticity, the character, the Conservative beliefs, the energy, the enthusiasm, the resilience.
“All the characteristics that are needed to make a truly great Prime Minister. Actually, if Suella wins we will both get the Prime Minister that we want.”