Age Concern Birmingham, one of the biggest members of the Age Concern federation, has suggested that some ACs might combine to form a new organisation under the existing brand.
"It is not inconceivable that many Age Concerns would prefer to retain the name and create a new national organisation that does not live under the major constraints of the current federation," it said in a letter to Catherine McLoughlin, chair of Age Concern.
A spokesman for Age Concern said there was no evidence to suggest that a rival national organisation might be established. "The vast majority of Age Concerns that have expressed a clear view are saying they want to share a strong new brand with a national partner," he said.
"If a minority of Age Concerns choose to retain the existing brand, they may find that, without a national partner, the strength of the brand declines dramatically."
ACs have also queried the cost to local groups of rebranding under a new name.
The spokesman said the new charity would support Age Concern members with the costs of rebranding.