Mr Mackay has said private schools can apply to local authorities for rates relief after he was contacted by Education Secretary John Swinney on behalf of Kilgraston School in Perthshire.

The SNP’s political opponents last night accused Mr Mackay of “passing the buck” to hard-pressed councils to mitigate his plans to end business rates charity relief for private schools.

They also claimed that Mr Swinney’s intervention showed that the SNP was divided on the issue.

Mr Mackay made the suggestion after Mr Swinney, the MSP for Perthshire North, wrote to him when he was contacted by a constituent, Thomas Steuart Fotheringham, a governor of the all-girls boarding school in Bridge of Earn. Private schools have expressed concern that hiking their tax bills will drive up fees, making independent education too expensive for many parents.

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Critics of the tax rise claim it will put more strain on the state school system if parents are forced to take their children out of the private institutions.

The Scottish Government has signalled that it intends to press ahead with the recommendation of the Barclay Review of business rates to end charity relief for private schools.

Charity business rates relief is almost entirely funded by the Scottish Government and private schools have been able to reduce their business rates bills by 80 per cent.

In his reply to Mr Swinney, the Finance Secretary suggested that once charity relief has ended private schools could make use of council powers to give rates relief locally. Mr Mackay also said he appreciated Mr Swinney would want to “keep a close eye” on the subject “given your dual role as a constituency MSP as well as Cabinet Secretary for Education and Skills”.

In the letter, which has been obtained by The Scotsman, Mr Mackay said private schools could apply for relief from councils under the Community Empowerment (Scotland) Act 2015. Mr Mackay’s letter said: “There would be merit in informing Mr Steuart Fotheringham that when developing business rates reliefs I am fully aware that national incentives are not always nuanced enough to fully flex to the needs of every sector and location. That is precisely why in 2014 I created a new power to allow councils the ability to offer bespoke local business rate relief schemes.

“Under section 140 of the Community Empowerment (Scotland) Act 2015 each local council has wide-ranging powers to create rates reliefs to reflect local needs. This may apply to a sole business, sector or area and, for example, could be utilised to support independent schools where the council believes the local economic benefit is sufficient to merit such an intervention. The relief may be an adaptation of an existing national relief scheme or a unique standalone scheme.

“Mr Steuart Fotheringham may wish to approach the council to request that they explore all avenues open to them to support his arguments and I emphasise that it is incumbent on the council to give any such request proper and full consideration.”

The Scotsman understands that the issue is being looked into by the Scottish Council of Independent Schools.

Last night shadow finance secretary Murdo Fraser attacked Mr Mackay.

Mr Fraser said: “Derek MacKay’s tax grab on independent schools is another example of this government’s short-sighted thinking. Rate relief currently allows independent schools to run bursary schemes that help to widen access to the sector.

“The SNP’s plans threaten to destroy that. This letter reveals that Mr Mackay is once again preparing to pass the buck to councils. Having already slashed funding to local authorities, he now appears to be demanding that they pick up the tab and mitigate his own tax-grabbing plans. It is outrageous.”

“The fact that John Swinney has raised concerns about this shows the divisions within the SNP about this proposal. The question now is whether he is now going to simply lie down and accept Mr MacKay’s tax grab, or stand up and fight against it.”

Mr Mackay’s approach was also criticised by Dorothy MacGinty, the Kilgraston head teacher. Mrs MacGinty said: “Mr Mackay has pointed out to John Swinney that actually there is still a route for independent schools still to get the 80 per cent rates rebate through the council.

“It is almost as if they are passing the buck. They are going to make this headline statement which garners great favour among the general population who don’t send their children to independent schools. But at the same time they are saying actually we’ll just pass it on to the local council and let them deal with it when they are already putting them under pressure.”

A Scottish Government spokesman said: “We are certainly not passing the buck to local authorities and have in fact given them greater powers over rate reliefs to allow flexibility to local needs. We accepted the independent Barclay review recommendation that reduced or zero rate bills relief for independent schools across Scotland was unfair on state schools and should be removed.”

Derek Mackay accused of passing the buck on private school tax changes