Analysis has found thousands of parish and town councils increased their share of the annual bill, raising £18.9m in extra funds.
The government said it could make them “subject to the referendum principles.”
But parish councils said that would be a threat to democracy.
Figures show 3,659 parish councils raised the basic Band D tax bill by more than 1.99%, the referendum threshold for larger councils.
Sixty small authorities at least doubled residents’ bills last year. Another 130 put their bills up by between 50 and 99% while 1,001 increased the annual bill for a Band D home by £5 or more.
Larger authorities and other bodies, such as police and crime commissioners, have to hold a referendum if they want a rise of 2% or more, or would raise bills by £5 per year per household. Parish councils are not subject to the same cap. This year, for larger councils, the threshold will be 3.99% as long as most of the increase funds adult care.
Some parish councils now planning large percentage increases for 2016-17, such as Sandbach Town Council in east Cheshire. It will raise its share of the council tax by 30%, about £18 a year for a Band D household.
A Department for Communities and Local Government (DCLG) spokesman said, “Town and parish councils should protect their taxpayers from excessive council tax increases; if they fail to do so, government has the option of making them subject to the referendum principles in future.
“This government is determined to keep council tax down with average council tax bills set to be less in real terms in 2020 than they were in 2010.”
The spokesman would not say whether there was a percentage rise threshold in mind for parish councils.
Defending the proposed rise, Sandbach Labour councillor Sam Corcoran said, “It’s a large percentage increase but it’s a small absolute increase. We’ve had our grant cut from Cheshire East Council, but more importantly, we’ve got some exciting plans to redevelop the town centre, which will go out to consultation.
“If we decide not to go ahead, we will give the money back again.”
One parish council chairman said the threat of a referendum would be bad for democracy.
Winchfield Parish Council in Hampshire, which has 260 homes, increased its council tax bills by £67.16 for Band D properties last year, raising them from £19.98 to £87.13. It was the largest rise in cash terms in England. The parish council’s share is on top of a further £1,408 split between Hampshire County Council, the fire and rescue authority, police and crime commissioner and Hart District Council.
The council said it did so in order to fund planning consultants to help it challenge Hart District Council’s plan for 5,000 new homes.
Chairman and Conservative councillor Andrew Renshaw said, “Parish councils are the closest of all authorities to their community and are responsive to how their electors feel. If they feel we should be spending this sort of money, we should have the right to do so and it would be bad for democracy to take that right away.”
Councillor Ken Browse, the chairman of the National Association of Local Councils, said parishes had increased their charges to pay for services, which had been withdrawn by larger authorities.
He said, “Local (parish and town) councils have been stepping up to the plate to take on a range of discretionary services which principal councils simply cannot afford to run any more – important local services and facilities such as libraries, toilets, youth work, community buildings and economic development activity.
“Add this to an already extensive range of visible services – like bus shelters, maintaining commons and open spaces, crime and community safety measures, running events and festivals, providing leisure and sports facilities – the average local council costs just £50 a year, less than a pound a week.”
Some parishes are also planning further rises from April, after taking on services previously run by district or county councils.
Newquay Town Council will put its council tax precept up 90%, adding £100 to a typical annual bill.
Frodsham Town Council in Cheshire is increasing its precept by 50%, equivalent to about £20 a year more for a Band D house.
Its chairman, Michael Pusey, said a referendum or a cap would put it out of business.
He said, “We’ve basically taken everything out of the piggy bank. If something went wrong, like a play area got vandalised, anything like that, we would not be able to do it. We need reserves to be able to do these things.”