Dominic Raabwho was deputy prime minister in Mr Johnson’s government, believes he will be “swamped up” by a Privileges Committee inquiry into his use of party gateways within days of returning to power.

He suggested it would drag the country into “a kind of Groundhog Day at the party” and make it difficult to move forward with a number of pressing issues.

Mr Raab also told Times Radio: “The challenge now is that within days of us having a new Prime Minister, which is no later than next Friday, the Privileges and Conduct Committee will start taking oral testimonies, including from Boris, as well as other witnesses.

Former Deputy Prime Minister and Minister of Justice Dominic Raab. Photo: Joe Giddens/PA Wire

“And it seems impossible to me for anyone to be prime minister who is absorbed, who is distracted and involved in the next saga or episode of the soap opera that is the party, and at the same time gives the country the attention that he requires.

“We would go back to Groundhog Day with partygate, we have to get the country and the government moving forward.

“I would like to hear the answer to how you can give evidence, how you can conduct these Privileges and Conduct Committee evidence hearings and at the same time be prime minister, giving the country, the economy, NHS, the relentless laser focus he needs. I did not hear the answer to this question. If someone thinks he can give it, he needs to explain it very clearly, or Boris does it.”

Mr Raab, who is backing former chancellor Rishi Sunak for the Tory leadership, told BBC Breakfast: “I think it is very clear that Rishi has the widest appeal because, and this is very important, he can restore trust. I think he is the best fit to restore the confidence we so desperately need.”

Mr Johnson’s return would face challenges, not least an investigation into whether he lied to the Commons about the partying scandal, for which he was fined by the police.

If he is found guilty by the House of Commons Privileges Committee, he could face impeachment proceedings, leading to a battle for a seat in the House of Commons if he receives a suspension of 10 days or more.

His popularity with the public has fallen, even though he is still high on friendship with the Tories.

Some MPs have even suggested that they may resign as party leader if he wins.

Commons Leader Penny Mordant is the only candidate who has so far officially announced his participation in the elections.

Dame Maria Miller, a Mordaunt supporter, believes Mr Johnson must be considering whether it is “appropriate” for him to run in the leadership contest.

She told BBC Breakfast: “I certainly think so Boris Johnson will think very long and hard about whether it would be appropriate for him to nominate himself and lead our country at a time when…he is still under a very serious investigation by the Privileges Committee, which could ultimately lead to he will have to leave the post of minister.

“I’m sure that he, who put our country first in his life, even when he was sick and in hospital during the pandemic, would not want to jeopardize the stability of our country – again, that’s why I support Penny Mordaunt, because I think it brings that stability.

“She can reach out to people who really need to know that they have someone at 10 Downing Street who really understands the struggles of ordinary people in this country.”