Boris Johnson becoming prime minister would increase the “urgency” for the Scottish Conservatives to reposition themselves away from the UK party and become a more autonomous sister organisation, a Tory MP has suggested.

As Theresa May comes under more pressure from within her own party to name the day of her departure from No 10, Conservative minds are turning to who should succeed her.

A new poll for the Conservative Home website, involving 1,128 people, suggested the former Foreign Secretary was now the clear favourite, polling almost a third of party members at 32.4 per cent; up by 10 points on a similar poll last month. Mr Johnson’s nearest rival was fellow Brexiteer Dominic Raab, the former Brexit Secretary, who polled 14.7 per cent.

But the prospect of the Old Etonian becoming PM has left several Scottish Conservatives aghast with some believing a Johnson premiership would be a gift for Nicola Sturgeon and the SNP and would “kill off” Ruth Davidson’s chances of becoming First Minister in the 2021 Holyrood poll.

Stephen Kerr, the Tory MP for Stirling, dismissed the Conservative Home poll as having asked a section of activists, who were not representative of the party as a whole, but admitted Mr Johnson was a “tremendously engaging person”.

“Let’s face it Boris is a celebrity politician…If you wanted a dinner guest to enliven your evening, you’d definitely have Boris to dinner. But does that necessarily make him the person you want to be prime minister? I would venture not.”

Mr Kerr suggested Mr Johnson had never cultivated an image among Scottish voters, who did not view him as an attractive figure. Indeed party sources have suggested to The Herald that during the 2014 independence referendum campaign the London MP was deliberately kept out of Scotland for fear his presence would have a negative effect on the No campaign.

The Stirling MP warned that if Scottish Tories did not create enough of a distinctive brand, then they could become “absorbed in some of the backwash from having Boris Johnson as leader”.

Although he made clear that the “stop Boris” mood within Tory ranks at Westminster was such that he did not believe the 54-year-old politician would succeed Mrs May as leader. Indeed, Scottish Tories have established “Operation Arse” to try to prevent Mr Johnson from ever becoming PM.

Stressing this was his own personal view, Mr Kerr said the Scottish party should already be a distinctive entity and have a relationship to the UK party similar to Germany’s right wing CDU/CSU parties.

The backbencher added: “We’re Conservatives who share some of the same common principles and values but we are distinctive because we are Scottish Tories and Unionists. In the minds of some people in the party, a Johnson premiership probably would make it more urgent[to become more autonomous]. It would be a repositioning of the Scottish Conservative and Unionist Party within the Conservative family…”

Last night, the executive of the Tories’ 1922 Committee met to discuss changing the rules to allow the party a vote on whether Mrs May should continue as leader; technically, she cannot be challenged again until December after winning a confidence vote four months ago.

Senior Tory backbencher Nigel Evans, an officer of the 1922, called on the PM to announce her resignation “straight away” to enable a contest to choose her replacement to begin.

The Lancashire MP said: "I hope she does accept the fact the call for her resignation now is growing into a clamour.”

It is thought bad results for the Conservatives in the forthcoming English local elections and the European elections, if they took place, could spell the end of the PM’s premiership.

However, Rory Stewart, the UK Prisons Minister, rallied behind Mrs May, claiming she was "our best hope" of resolving Brexit.

“The problem is not the Prime Minister, the problem is Brexit," he declared.

Some 70 local Conservative association chiefs have signed a petition calling for an extraordinary general meeting of the National Conservative Convention to discuss the PM's future.

One signatory, Greig Baker from Canterbury, said: "Removing Theresa May has become like a trip to the dentist; it's something that's got to be done and the longer you leave it, the worse it will be."