Mr Swinney told the Scottish Parliament the scheme would be “proportionate” to one in England where about £500m has been made available. The move is an attempt to break the impasse over the 35,000 equal-pay cases lodged with tribunals in Scotland.

Councils will apply to the Scottish Government but the money will then have to be secured from a body such as the Public Works Loan Board, an executive agency of the Treasury.

Mr Swinney said the Scottish Government would try to accommodate as many of the requests for assistance as possible, but warned: “There is never a blank cheque from Her Majesty’s Treasury.”

He made the announcement during a debate on the findings of an inquiry by Holyrood’s Local Government Committee into equal-pay costs, published in June. At the time, the estimated bill for councils for meeting single-status and equal-pay claims ranged from £340m to £1bn. Of Scotland’s 32 councils, 26 have equal-pay agreements and five are “on target” to do so by the end of the year.

Mr Swinney said the scheme would be introduced in the current financial year.

Labour MSP Duncan McNeil, convener of the Local Government Committee, said many of the unresolved cases affected low-paid female workers. He said the process had become “litigious” and called on the Scottish Government to intervene with councils, unions and lawyers.

The inquiry had been “deeply frustrating”, he said. “If it’s been frustrating for us, just imagine what it’s been like for those workers who haven’t been properly compensated. We must ask, is it because they are low-paid women workers?”

Sarah Boyack, Labour MSP for Edinburgh Central, said local authorities were compounding the problem with plans to allow private firms to run home-care ­services. “Women are predominantly the vulnerable clients and they are predominantly the hard-working care staff.”

Margaret Mitchell, Tory MSP for Central Scotland region, said: “There are real fairness issues here.”

One MSP said the ­behaviour of councils and unions was unacceptable, and fiercely denounced a firm of lawyers involved in equal-pay claims. Tricia Marwick, SNP MSP for Central Fife, attacked “no-win, no-fee” lawyers, in particular the Newcastle-based Stefan Cross firm. “I have found the actions of the no-win, no fee lawyers quite despicable,” she said. “They have exploited these women just as much as the councils or anybody else.”