Councils will seek legal advice on how to avoid implementing the proposals to increase white-collar compulsory competitive tendering (CCT) if their request for new legislation is ignored.
Officials from the Association of Metropolitan Authorities (AMA) and other council associations told civil servants at a meeting earlier this month that the white paper's proposals would be impossible to implement unless new legislation was introduced.
But environment minister Sir Paul Beresford said there was not enough time to introduce legislation before the next general election.
The white paper has been the centre of controversy since it was published in May, and the AMA threatened legal action earlier in the year over the proposed timescales for speeding up CCT.
The current problems began when a confidential paper drawn up by civil servants was leaked to the press before this month's meeting.
It proposed a more radical overhaul of the credit and allowances system than was originally anticipated.
The system currently allows councils to count some of the services they buy from the open market, such as counsels' opinions, as part of the tendering targets they are required to meet.
But the leaked paper indicates that goods and services such as computers, legal advice and work from other departments in the council would be removed from the system. This would greatly increase the amount of in-house work councils would have to tender out.
Kirsten Gillingham, senior manager of the chartered institute of public finance of accountancy, which advises councils on competition matters, said the proposals were causing confusion and uncertainty among local authorities.
She said: "If the proposals are so radical that consultation is not enough, then local authorities will demand more scrutiny in Parliament.
"If they don't get new legislation, and the changes appear to contradict the original legislation, then they might seek to get round implementing the changes.
"At the moment local authorities feel that any decisions they make about CCT could be invalid in six months."