Danny Alexander has effectively accused Scottish ministers of failing to investigate how many civil servants in Scotland have their salaries paid into private companies.

It follows a Treasury review that found more than 2000 staff employed by UK Government departments and agencies were "off payroll" – potentially allowing them to reduce their tax bills.

Mr Alexander, the Chief Secretary to the Treasury, said the remit of his review did not include Scottish Government bodies.

He has written to John Swinney, the Scottish Finance Secretary, urging him to act.

It follows a number of cross-Border rows between Mr Alexander and Mr Swinney in recent months, including plans to reform public sector pensions and the potential economic effects of independence.

In his latest correspondence to Mr Swinney, Mr Alexander writes: "It is critically important that people in Scotland have confidence that the Scottish Government employees are not in a position to avoid tax, and that there is transparent disclosure of current arrangements to support this.

"I would be grateful if you could let me know when the Scottish Government will be undertaking a similar review, and that you will pass all the detailed findings to HMRC."

A Treasury source said that it was impossible to know the scale of the problem in Scotland.

"There is absolutely no reason to think that this is not proportionally as widespread as this is in England, which is where our review was mainly focused," he said. "There should be greater transparency and we don't know what the delay is."