It means some of the country’s best known schools like Heriot’s, Watson’s, Gordonstoun and Fettes College could face bills running into six figures.

Bosses at fee-paying schools have previously warned it would place Scottish education at a competitive disadvantage in the UK and globally.

Some of the countrys best known schools like Heriots could face bills running into six figures.

John Edward, director of the Scottish Council of Independent Schools (SCIS) said: “The announcement is, pure and simple, a backwards step by the Scottish Government - taken against advice and evidence from many quarters.

“If followed through, this proposal will weaken and narrow the widening access programme and, most importantly, it will impact on those accessing bursary assistance made possible by the reduced rates level.

“It is dispiriting to learn that the Government considers that independent schools and their parents alone are deserving of a targeted fivefold rates rise.”

About 50 schools across Scotland will be affected. In Edinburgh, it is estimated that private schools educate about 15-18% of children, with Stewart’s Melville and Merchiston Castle among their number.

The move won’t be implemented for several years as schools are given a period to prepare for the changes.

The schools had previously enjoyed 80% relief from business rates, along with other institutions like universities and special schools for youngsters with disabilities. Council arms length bodies which run leisure and arts facilities also enjoyed the relief.

A review of Scotland’s business rates by former RBS chief Ken Barclay recently called for the relief to be scrapped on all these bodies. But Mr Mackay announced yesterday only fee paying schools will be hit by the change.

“It is our assessment that without this relief non-domestic rates will be fair and sustainable for the independent schools sector, as they are for other types of organisation occupying non-domestic property,” a Scottish Government spokeswoman said.

Specialist schools like music schools could also continue to enjoy the exemption.

Across Scotland private schools educate more than 30,000 pupils, employing 3,500 teachers and the equivalent in support staff.

Tory education spokeswoman Liz Smith branded the move a “blatant attack” on the independent school sector.

“For a party that is supposedly in favour of widening access this move will make independent schools more elitist and less accessible to those from poorer backgrounds,” she said.

“That will be met with dismay by those parents whose sons and daughters have been in receipt of increasingly generous bursary support.”

Private schools have faced previous calls to be stripped of their charitable status in Scotland, but escaped this after making improvements in widening access and diversity. Yesterday’s move will not affect this status, but remove their eligibility for rates relief.

The decision to allow special schools to remain exempt was welcomed by the Royal Blind School in Edinburgh.

Mark O’Donnell, Chief Executive of Royal Blind said: “If the Royal Blind School had become liable to pay business rates this would have resulted in an additional cost of over £100,000 a year to the school.”

The decision to spare universities was also welcomed.

“This is a sensible approach and allows universities to help grow Scotland’s economy,” a Universities Scotland spokeswoman added.

Scottish Budget 2017: Private schools hit with Â£5m rates hike