Anti-poverty charity Turn2us said the impact of the pandemic has left many people in "financially precarious" positions, with even more expected to seek support in the coming months.
Low-income households and pensioners in England can apply for a discount or exemption on their council tax under the Council Tax Reduction scheme.
In Preston, 8,949 working age residents were claiming support in the three months to June, Ministry of Housing, Communities and Local Government figures show.
That was the highest number for any quarter since 2015-16, when comparable records began, and an eight per cent rise compared to the same period last year.
Meanwhile, the number of pensioners claiming a council tax reduction fell to 3,827 from 4,065.
Across England, the total number of claimants reached 4 million between April and June, up from 3.9m in 2019.
The Council Tax Reduction scheme replaced the nationally-administered Council Tax Benefit in 2013, giving individual local authorities the power to decide who is eligible for support and what discounts to offer.
Sara Willcocks, head of external affairs at Turn2us, said the change means "more people than ever" are paying local taxes.
She added: "While it is good news that there has been a modest uptake in people getting discounts on their bills, there are still thousands who are missing out.
"The coronavirus pandemic has pushed millions into financially precarious positions. We expect to see more and more people need this benefit over the next few months.
"Local councils must be supported by Westminster to end the postcode lottery with council tax support so that they have the money and resources to help people struggling."
The Institute for Fiscal Studies warned in a recent report that large falls in council tax and business rates revenues will hit local authorities' spending capacity this year.
Separate figures from the MCHLG reveal in the three months to June, Preston City Council raised £20.7m through council tax – down from £20.8m over the same period in 2019.
It was a similar picture across the rest of England, where council tax revenue over the three months fell to £9bn, from £9.1bn last year.
Richard Watts, of the Local Government Association, said a rise in claims for council tax support was expected, and councils are putting in "a wide range of measures" to help residents facing financial hardship.
“However, councils are facing increased cost and demand pressures at the same time as experiencing a significant drop in income," he added.
“The funding already received from the Government has been a positive step and recognises the crucial role councils have played in keeping the country going throughout the pandemic."
Extra cost pressures on local authorities must be met by the Government to avoid cuts to services, however, Mr Watts said.
A Government spokesperson said: “We’re giving councils unprecedented support during the pandemic.
"This includes £4.3bn funding, compensation for irrecoverable income losses and a scheme allowing them to spread their tax deficits."