Hull councillors had to start paying after the insurance provider went into liquidation.
City councillors have been warned they might have to stump up more cash to settle historic compensation claims over asbestos-related illnesses.
The authority has paid a total of £3.5m in two separate pay-outs since 2014 to meet liability requirements following a court judgement two years earlier.
Rather than payments to individuals, the pay-outs were in the form of levy charges imposed after the council’s main insurance provider Municipal Mutual Insurance (MMI) went into liquidation in 1993.
The levy charges are pooled into a national pot which is then used to settle asbestos-related compensation claims.
Legal wrangles over liability issues following the liquidation of MMI went on for nearly a decade.
But in 2012, the Supreme Court ruled the insurer was liable to pay outstanding compensation to employees who had contracted mesothelioma, a fatal type of cancer linked to exposure to asbestos.
As a result, a so-called scheme of arrangement was triggered requiring councils such as Hull to pay levies into the national pot based on a percentage of the amount paid to creditors.
Hull paid just over £2.1m in early 2014 as a result of the ruling.
Then, following a further review of MMI’s financial position, the levy was increased from 15 per cent to 25 per cent.
Hull then provided another £1.4m to fund the additional levy.
Now, the city council’s chief finance officer David Bell has warned the authority might have to dip into its pockets once again.
In a new report, he said: “The scheme’s administrators have advised that it is possible that a further levy may be required to meet future cost but at the moment none is payable and, as such, further liabilities cannot be reliably quantified.”