Research by the Local Government Chronicle - which received responses from 262 of the 353 councils - found that speculation over a tighter limit had influenced behaviour. Some 14% of councils changed their proposals as a result, with half now planning a tax freeze.
Confirmation of the figures will not come until spending plans have been approved by council meetings across the country over the coming weeks.
Councils want to freeze tax for their residents, but many local authorities are under increasing pressure as a result of cuts to their government grant and rising demand for their services.
The fact that so many have chosen to increase tax by around 2% rather than accept government funding equivalent to a 1% tax rise is a sign of just how stretched councils are.
– LGC editor Emma Maier said:
Local authorities face a 2.9% cut in overall Government funding for 2014/15 - another reduction to budgets which town hall leaders say are already too stretched to pay for some important services.
Dozens of English councils are poised to infuriate ministers by raising council tax just short of the threshold that would trigger a referendum.
Almost a third of authorities will reject extra central Government funding equivalent to a 1% rise to help them freeze bills, according to the most recent survey, and more than half of those plan to impose a hike of 1.99%, the biggest possible without being forced to seek the approval of voters.
Communities Secretary Eric Pickles - whose desire to halve the cap to 1% was blocked by the Liberal Democrats - has described town hall leaders who go close to the limit as "democracy dodgers".
Evidence that one in three councils make more by charging for some services has come under fire from accountants working in the public sector.
The Chartered Institute of Public Finance and Accounting (CIPFA) suggested the Audit Commission has called on the Government to set up an "independent grants commission" to help ease problems with local authority funding.
The chairman of a regulatory body overseeing the public purse has distanced himself from evidence showing some councils make more money by charging for additional services than council tax.
Audit Commission chairman Jeremy Newman said there was no "one-size-fits-all" formula for how councils decide which services they charge for.
A rise in the money generated by charging showed "the significant role" it was now playing in funding public services.
There is no 'one-size-fits-all' formula for how councils set their local charging policies. We are providing information and tools for councils, and those who hold them to account, to help understand the important role that charging plays in councils' strategic financial management.
The fact that some bodies derive more income from charging than council tax is neither good nor bad, but highlights the significant role charging plays in funding public services, and reminds councillors and electors to carefully scrutinise the approaches councils are taking.
Existing bin polices are "barmy" according to Communities Secretary Eric Pickles.
In the run up to new guidance published next week on where to put wheelie bins and recycling boxes, Mr Pickles said:
This Government is standing up for hard-working people and getting rid of barmy bin policies which made families' lives hell. I want to make sure families get a proper rubbish and recycling collection service for the large amount of money they have to pay in council tax.
For years, badly-placed wheelie bins and the proliferation of multiple bins have created a blot on the landscape....By ensuring that developers create appropriate waste storage areas when designing new homes, we can tackle the ghastly gauntlet of bin blighted streets and driveways.