The Scottish Conservative leader called for major institutions - such as the British Museum - to consider setting up elsewhere in the UK, as well as for most fishing infrastructure to be moved to Scotland.
Ms Davidson also suggested that more government posts should be spread around other parts of the country.
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She will deliver a speech on the union at the Policy Exchange in London on Monday, a day after SNP leader and First Minister Nicola Sturgeon promised to “restart the debate” on Scottish independence with the publication of her party’s long-awaited growth commission this Friday.
Writing for the Financial Times, Ms Davidson said the report, which will set out policy options for an independent Scotland, demonstrated the union “remains under threat”.
She said that it was “unlikely” that the latest drive would be met with enthusiasm, but warned against “complacency” and “indifference”.
“As long as our future relationship with the EU is in flux, it would be foolish to assume that the current trends on Scotland remaining in the UK will hold and that the threat of separation has gone away,” Ms Davidson said.
“The SNP is in power north of the border and will use that clout to drive a wedge between Scotland and the rest of the country.
“So we unionists must work hard to bolster our case for the union.”
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Ms Davidson urged the UK Government to “develop better practices” to recognise the reality of devolution and build relationships with Edinburgh.
She continued: “We also need to spread the benefits of the union fairly and equally around the nation. The UK is still too London-centric.
“As befits one of the world’s great cities, the capital gobbles up talent, money and status.
“It is government’s job to ensure that more of this ends up in the other great British metropolitan areas in our regions and in our nations.
“The Conservative government in Westminster is already delivering on its manifesto promise to move Channel 4 out of London.
“But this should be just the start. More cultural institutions - like the British Museum - should set up second homes outside the capital. More government posts should be based in other parts of the UK.
“With Brexit, we have an opportunity to ensure the powers that return to these shores are based nearer the communities they serve.
“Most of the UK’s fish, for example, are caught in waters off Scotland. So I believe most of the UK’s fishing infrastructure should be based north of the border.”
Ms Davidson insisted it was “not an anti-London argument”, pointing to the success of the 2012 Olympics in “allowing Britons to feel they had a stake in their country”.
“That should be our goal so people, including those who currently support independence in Scotland, feel the UK is theirs too,” she said.
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