DAVID Cameron is today due to have his first face-to-face talks with Ruth Davidson since the Tories’ breakthrough in the Holyrood elections as the Scottish Conservative party leader made clear there was “not a chance” of her wanting to take over the leadership of the UK party when the Prime Minister decides to step down.

The two Tory leaders are expected to meet at a No 10 Lesbian/Gay/Bisexual/Transgender reception hosted by Mr Cameron; it is taking place on the eve of the International Day Against Homophobia and Transphobia.

Earlier this month in the Scottish parliamentary elections, the Scottish Tories surprised even themselves by gaining 31 seats, up 16 on 2011, and in so doing supplanted Labour as the official opposition at Holyrood.

Following the May 5 poll, the PM warmly congratulated Ms Davidson, one of the UK's most high-profile gay politicians, on the "historic result", saying his colleague would "stand up to the SNP and give Scotland strong opposition". Last week at PMQs, he lavished praise on his Scottish colleague for her “stunning performance”.

Last April, Mr Cameron fuelled speculation that Ms Davidson might one day become leader of the UK Conservative Party. When he was asked about such a prospect on BBC Radio Four’s Woman’s Hour, he replied: "Indeed. I don't put a limit on her ambition. She is extremely effective."

At last autumn's party conference, one senior ministerial source close to Mr Cameron talked up Ms Davidson's chances. When asked if she could be a potential candidate to succeed the PM, he replied: “If people want a strong woman candidate to succeed him, then Ruth is obviously a strong woman candidate.”

Last year, Heidi Allen, the Tory MP for South Cambridgeshire, said she wanted to see a candidate to succeed Mr Cameron, who offered a different kind of politics, and mentioned the Scots Tory leader.

“I want to see somebody completely new, I mean I’m a new MP so I’m still learning. People like Ruth Davidson, for example, are amazing.”

But the Scots party leader, speaking to ITV’s Good Morning Britain, suggested Mr Cameron was “being pretty clever” when he made the comments on Woman’s Hour.

“He picked the only person in the party that is not an MP in the Commons and, therefore, he wasn’t backing one colleague against the other,” she explained.

Asked whether she would be interested in the job as the leader of the UK Conservative Party, Ms Davidson exclaimed: “Not a chance,” adding: “I wouldn’t thank you for the job. I am hugely privileged. I have seen behind the door of No 10 and it’s a pretty lonely job and it’s not one that I seek after.”

However, Westminster-watchers have noted that politicians who are asked about the top job rarely respond positively and they have also pointed out that in recent years the favourite for the leadership role has invariably failed to win it.

Some Tories believe that if the party wants to broaden its appeal across the UK, then they need to look beyond the usual white patrician candidate and look to someone like Ms Davidson. While it has been noted how she would have to become an MP to stand in any future contest, it has also been stressed that this obstacle was removed quickly and easily for Boris Johnson, who is regarded as a potential future leadership contended once Mr Cameron decides to step down.

While the PM has made clear that, whatever happens in the EU referendum, he intends to serve a full term to 2020, few at Westminster believe this will be the case and a Tory leadership contest could take place as early as 2017.