Bird Aid said unless they secure funding or a grant by November 27, they will have to close their Hydeaway site off Hempstead Lane.
A Bird Aid spokesperson said, “This will result in dozens of disabled wild birds and other wildlife being euthanised as they cannot be relocated.
“These will include gulls, pigeons, ducks, guinea pigs, rabbits, chinchillas and ferrets.
“Rehousing all will not be possible owing to further reduction in wildlife outlets in recent times.”
Many people with learning disabilities who work at the site will also lose their job, according to the spokesperson.
The spokesperson said, “Future wild birds and other forms of wildlife will be neglected and abandoned.
“Finders will be left alone to take casualties to centres that will cease to exist.”