The private loans, often referred to as LOBOs, (lender option, borrower option) is a long-term finance package provided by banks, brokerages and intermediary firms to be paid back between 40 and 70 years.
The loans, which were mostly taken out prior to the financial crisis, provided councils with a 'cheap source of financing with low teaser rates' compared with the Government-run Public Works Loan Board financing available to them.
The interest rate is initially fixed, but unlike PWLB loans, private banks have the option to propose or impose - on pre-determined future dates such as every five years - a new fixed rate.
The borrower (the council) has the 'option to either accept the new rate or repay the entire loan - forcing to pay a 'breakage penalty' in return.
Figures show Sheffield Council last took out loans from BAE Systems 2000 Pension Plan Trustees Ltd in 2011 worth £25 million.
In the last 15 years, the local authority also took out a LOBO loan from Barclays at £30m and £20m from the Royal Bank of Scotland.
The loans have been criticised by Sheffield South East MP Clive Betts who said councils have 'entered into bad deals' and added Parliament should examine the relationships between the banks, brokers and consultants who sold the loans.
Sheffield Council said LOBOs make up 'for only 17 per cent' of all local authority borrowing
Sean Kemp, senior lecturer in banking and financial management at Sheffield Hallam University, said councils like Sheffield are now paying a 'high price' for previous financial decisions.
"Sheffield Council's decision to use LOBO loans is particularly worrying given their high interest rate," he said,
"These were initially a cheap source of financing with low teaser rates.
"Given that the PWLB loans were essentially from the government there is greater scrutiny of spending and the ability to repay this may not have been as rigorous at the commercial lenders such as RBS and Barclays.
"These LOBO loans are incredibly complex as it requires the buyer of such products ‘the council’ to be able to compare the risks and rewards. It is unlikely any of the councils would have been able to predict accurately these future costs of these loans compared with a standard loan arrangement.
"Councils around the country are now paying a high price for their decisions 10 years ago. Ultimately we the tax payer will bear the brunt of those costs while receiving less in terms of council services."
Eugene Walker, director of finance at Sheffield Council said: "The council borrows to invest in new schools, roads, buildings and other assets that provide long term benefits to the citizens of Sheffield.
"LOBOs - lender option borrower option - are part of our balanced loan portfolio which seeks to spread risk across a range of lenders.
"At present, they account for only 17 per cent of our loan portfolio. The cost of the loans will fall over time as we are no longer using them. Our last loan was taken out in 2011.
“LOBOs are not unstable. They have fixed interest rates, which, are reviewed periodically, and can be raised at the lender’s option. However the council then has the right to repay the loan.
"Our accounts, which contain details of these loans, are subject to annual scrutiny by our external auditors. They have not criticised our use of LOBOs, which have been used widely by many local authorities.”