The Scottish Conservative leader disclosed her fears when she spoke to the glossy fashion magazine and posed for a photo shoot with her dog Wilson.
With Theresa May struggling to keep the lid on Tory splits over the handling of Brexit, Ms Davidson was asked if she thought the Conservative brand would be “retoxified” following European Union withdrawal.
“My worry is actually much greater than that,” Ms Davidson replied. “My worry is that we’re about to head into a culture war around the world where it’s not a question of left versus right any more – it’s a question of open versus closed.
“We’ve spent a long time believing there was a consensus about the idea of freedom and interaction and breaking down borders, and then suddenly they’re all being built back up again. That’s what I think the fight is going to be about, and I’m damn sure going to take part in it.”
As a prominent Remainer, Ms Davidson has spoken of the need for a positive outcome from Brexit and in a speech last night underlined the importance of continuing to attract people to the UK after EU withdrawal.
On the subject of US president Donald Trump’s planned visit to the UK, Ms Davidson said she thought it was a “bad idea” and appeared to give tacit approval to those who choose to protest against him.
“Oh, I think it’s a bad idea [the Trump visit],” she said. “But maybe it’s one of those ones where actually you see the absolute best of the UK. ‘Because of the position you hold, not the man that you are, you can come here – but by God, because we’re free citizens we’re going to stand in the street and tell you what we think of you’. I’m not encouraging people to, but I would be surprised if they didn’t.”
Responding to speculation she is being lined up to replace Mrs May, Ms Davidson played down the suggestion.
“I am not going to be replacing Theresa May,” she said. “I’ve got a job to do in Scotland. I wouldn’t leave it to go and do another job. That’s not the way this is going to work. I am not the next leader of the Tory party.”
Ms Davidson spoke of the need for a positive approach to the challenges posed by Brexit when she delivered the David Hume Institute Lecture in Edinburgh last night.
Despite many voters choosing Leave in an attempt to reduce immigration, Ms Davidson spoke of the importance of attracting talent to the UK.
She said: “Freedom of movement from the European Union will end following the Brexit vote, but it doesn’t follow that, as some might have it, immigration is going to end.
“What Brexit means is that simply that the UK will design its own immigration rules for people coming into the country from the European Union. How we decide to exercise those competences is a debate we now need to have ... especially at a time of near full employment. We must not just be open to people coming to this country, but we must attract them too.”
She also called on the Scottish Government to concentrate on improving economic growth and advocated the establishment of a new environmental court based in Scotland and a new system of agricultural support.
Readers will be able to read her interview and see the full shoot in the March issue of Vogue, which goes on sale on Friday. The interview is also available online at http://www.vogue.co.uk.