Thousands more people are seeking debt advice as public spending cuts force an increasing number of poorer households into paying council tax.
And Conservative-run councils are the most likely to seek to impose bills on the least well-off households in their areas by "political preference", an economic think tank said.
They were among the main findings of an Institute for Fiscal Studies (IFS) report into the controversial move to end a national benefit scheme from April 2013.
It also raised questions about how much tax would go uncollected.
Local authorities were handed responsibility for designing their own systems but central government funding for them was cut by 10% at the same time to save £414 million.
With pensioners protected from the impact, most councils have passed on at least some of the reduction to low-income households which previously paid nothing or received help.
Town hall chiefs complain of being left in an impossible situation and a Commons spending watchdog has raised serious concerns about the impact on vulnerable households.
The IFS report - commissioned by the Economic and Social Research Council - said entitlements for 2.5 million working-age households dropped by an average £160 a week.
Minimum payments were introduced in deprived areas - mostly Labour-controlled - because they faced deeper reductions in funding, it said.
But stripping out factors such as the scale of cuts and proportion of protected OAPs in an area suggested that Conservatives were more likely to do so by "political preference".
On the IFS calculation, Tory-run authorities were 14% more likely than their Labour equivalents to do so and 25% more likely than Liberal Democrat councils.
In areas where a "significant" minimum was introduced there was a 30%-40% increase in July to September in the numbers seeking help from Citizens Advice bureaux about paying the tax.
That was t he equivalent of around 3,000 more individuals in 113 areas, the IFS said.
Of two million working-age households that would otherwise have been exempt from paying anything, 1.4 million now faced a bill - in a million cases of at least £85.
Half a million were liable to upwards of £170 and 200,000 for at least £225, the report found.
Senior research economist Stuart Adam, one of the report's authors, said: "Localising council tax support has, of course, led to considerable variation in the level of support available.
"Low-income working-age families are now likely to receive more help with their council tax if they live in a better-off area without too many low-income pensioners among their neighbours.
"Conversely, working-age people living in poorer areas and in areas containing more low-income pensioners receive less help."
Co-author Robert Joyce said: "Introducing minimum payments has increased the number of people seeking advice about council tax debt.
"It remains to be seen how successfully the local authorities concerned manage to collect the council tax that they have asked for."
Local Government Minister Brandon Lewis said: "Spending on council tax benefit doubled under Labour and is costing taxpayers £4 billion a year - equivalent to almost £180 a year per household.
"Our reforms to localise council tax support now give councils stronger incentives to support local firms, cut fraud, promote local enterprise and get people into work. We are ending Labour's something for nothing culture and making work pay.
"We have protected pensioners from any change as they have fixed incomes and cannot reasonably be expected to go back to work. Pensioners who have saved and worked hard all their lives deserve dignity and security in retirement."