Some 74% of local authorities in England are planning to increase their demands on families whose council tax is currently discounted or even covered in full by the Government.
From April, however, the system of council tax benefit will be scrapped and authorities asked to introduce their own council tax support scheme, but with a 10% cut in funding.
The study by the Resolution Foundation independent research group found that some councils were planning to charge affected households an extra 20% of the full council tax bill. Some households faced increases in bills of more than £600 a year.
Researchers warned that a variation in rates of council tax support could undermine the Government's new universal credit, which is meant to simplify the welfare system and ensure it always makes financial sense to take a job.
The report's author, Matthew Pennycook, said: "The axeing of council tax benefit has major implications for universal credit, which is supposed to be all about simplifying welfare and giving people a stronger incentive to work.
"These changes undermine both goals. There will now be a highly-complex and confusing patchwork of local support while the low-paid will keep even less of an extra pound in earnings than the Government has claimed."
Gavin Kelly, chief executive of the Resolution Foundation, said: "Millions of England's poorest households - both in and out of work - are already very close to the edge given falling wages, tax credits and benefits.
"Very few of those currently exempt from paying the full rate of council tax are expecting a large new bill to drop onto their doormat this spring. When it does, they are going to find it hard to cope.
"The new system will result in hard-pressed councils spending scarce resources chasing some of the poorest people in the country for non-payment."
Local government minister Brandon Lewis said: "Spending on council tax benefit doubled under the last administration and welfare reform is vital to tackle the budget deficit we have inherited.
"Under the last administration, more taxpayers' money was being spent on benefits than on defence, education and health combined.
"Our reforms will localise council tax support and give councils stronger incentives to support local firms, cut fraud, promote local enterprise and get people into work. We are ending the 'something for nothing' culture and making work pay.
"Under the last government, council tax bills doubled. The coalition Government has worked with councils to freeze council tax for two years, with a further freeze offered for this year. We are cutting council tax in real terms for hard-working families and pensioners, and we are on the side of people who work hard and want to get on."