The New Local Government Network made its comments after Westminster and Bournemouth councils said they doubted they could control face-to-face fundraisers, also known as 'chuggers', under the act.
The act states that charities should apply first to the Charity Commission for public collections certificates and then to local authorities for permits.
Permits can be refused only if chugging would cause "undue inconvenience to members of the public by reason of the day, week, date, time, frequency or locality in which it is proposed to be conducted".
The Public Fundraising Regulatory Association said it had received written assurance from the Office of the Third Sector that the new rules do not allow "vexatious" local councils to prevent fundraising if they simply don't like it.
But James Hulme, head of communications at the New Local Government Network, said councils could interpret the act differently, particularly the phrase "undue inconvenience".
He said that even if the act didn't give councils the powers they wanted to control chuggers, they could find other means.
"Councils could try to remove fundraisers on grounds such as antisocial behaviour, if they can prove they are a nuisance," said Hulme.
He said the concerns expressed by Bournemouth and Westminster had highlighted the confusion about the powers granted to local authorities by the act.
Contrary to reports in the press, Westminster is not seeking to ban chuggers.
But a council spokesman said it was lobbying government to bring forward the provisions of the act from 2009 so it could take a firmer line under the permit system.
"Chuggers are an irritant, and our councillors know this from their postbags," he said. "But we are not seeking a ban. Councillors want to use the new powers simply to improve the area."
Roger Parker, the town centre manager for Bournemouth, said his council planned to seek extra local powers to restrict what it considered to be inappropriate fundraising methods. He could not say what the definition of "inappropriate" would be.
Mick Aldridge, chief executive of the PFRA, has requested a meeting with Westminster councillors to discuss their concerns.
"We can only assume Bournemouth has misinterpreted the new legislation," said Nik Earl, communications manager at the association. "The act puts the responsibility on all local authorities to facilitate responsible fundraising."