The former prime minister, while not naming individuals, said “routine attacks” on Theresa May “in the most lurid fashion” were unacceptable and damaging to the national interest during the Brexit talks.
Mr Johnson has been a vocal critic of the prime minister’s Brexit policy, after sensationally resigning from the cabinet in July in protest at her Chequers plan.
On the eve of the Conservative Party conference, the ex-foreign secretary published a lengthy article setting out his own Brexit plan and also repeatedly refused to rule out challenging Ms May for control of the party or voting down a deal with the EU.
His antics have divided the party, rallying some hardline Eurosceptics to his side but infuriating other Tory MPs. His former deputy at the Foreign Office, Sir Alan Duncan, said he craved publicity like a drug addict needs cocaine.
Sir John, who was prime minister from 1990 to 1997, said those challenging Ms May were “inexperienced”, adding: “When I look at the alternatives to the prime minister, I am drawn even more closely to her.”
Speaking at an event in South Shields on Friday alongside the former Labour foreign secretary David Miliband, he said: “I do not think routine attacks on the PM in the most lurid fashion are either the spirit of politics that one would wish to see, or in the interest of the negotiating posture of the United Kingdom.”
Sir John added that “the threats that come in her direction of a leadership election unless she delivers a certain sort of Brexit ... [went] far beyond anything that I would think was remotely acceptable in behaviour towards any prime minister”.
He also pointed to the “inability of those who level these taunts to actually come up with any coherent plan of any sort themselves”.
Sir John also set out his support for a fresh referendum on the Brexit vote, claiming the public should be allowed another say as Leave presented a “fantasy case” at the 2016 referendum.
He said the argument that a fresh vote was undemocratic was “a rather curious proposition” and he could not see an “intellectual argument” against rerunning the ballot.
The Independent is calling for a Final Say vote on any future Brexit deal, which has attracted the support of more than 820,000 people.
Brexit rows are set to dominate the Conservatives annual convention, which begins in Birmingham on Sunday.
Mr Johnson is likely to be a major draw for party members – and a thorn in Ms May’s side – as he makes a rival address from the conference fringe on Tuesday.
Speaking to the BBC on Friday, the Uxbridge and South Ruislip MP was asked repeatedly to rule out running against her.
He said: “The prime minister will go on, as she said to us herself, and as she said to the country, she’s a remarkable person, she will go on for as long as she feels it necessary.
“But the most important thing for me is to avert what I think would be a political and economic disaster for this country, which is to agree to come out of the EU but still to be run by the EU – what is the point of that, what will we have done?
“And I think there is still time for her to change course.”
Political opponents attacked his efforts and dismissed his plans for a “super-Canada” Brexit deal as unworkable.
Sir Alan, a Foreign Office minister, told The Spectator: “There was only room for one showman in the Foreign Office. I get on with the diplomacy.
“But for Boris? Publicity is his cocaine. He needs a regular fix. And he equates getting publicity with having political power and authority and respect.
“But I think what he doesn’t realise is that whereas he used to be an electoral asset, that is now waning.”
Ex-cabinet minister Nicky Morgan told PoliticsHome that Mr Johnson’s timing was deliberate, saying: “He knows how important the party conference is to the prime minister, to the party, and it’s obviously designed to make it clear that, yet again, we will be talking as much about Boris as we will about the Conservative programme for government next week.”
However, his plan was defended by fellow hardline Brexiteers including Jacob Rees-Mogg, who likened the prime minister’s Chequers blueprint to the Charge of the Light Brigade, saying it was “a brave and mistaken dash against all the odds”.
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