sheffield and Leeds have warned the biggest lobby group for councils they could resign as members.
The pair joined the rest of the Core Cities group, comprised of the biggest English cities outside London, in giving notice on their membership of the Local Government Association.
In a statement, the Core Cities said that while there were issues that face all local authorities there were matters which “affect large urban areas differently, and on which we need to have more focused representation at the national level.”
It continued: “We feel there is an immediate need to increase engagement and representation by and for the Core Cities, particularly on issues of devolution for economic recovery and growth.”
Losing the membership of the major English cities would cost the LGA around £600,000 in fees.
More significantly the resignations would damage its credibility as an organisation representing the interests of local government.
However, at this stage the cities have only given notice of their resignations which will not take effect for a year and it is understood further discussions with the LGA are likely to be held in the coming months and the threat may not be carried out.
An LGA spokesman said: “This time last year 31 councils were on notice to leave the LGA this April, and we are pleased to say that all 31 will now be remaining in membership.
“So far this year 16 councils have given notice to leave from April 2014 and this will increase to 20 if the remaining four core cities follow suit.
“Now more than ever it is important for local government to work together and to speak as one national voice. We will continue to work closely with the core cities, individually and collectively over the next 12 months, to ensure that our membership offer meets their needs and expectations.”
Earlier this year the leaders of the Core Cities councils announced they were creating their own “cabinet” focused on finding ways cities could contribute to economic growth.