The site in Coundon Wedge Drive, Coventry, is run independently to the national RSPCA and said it costs £40,000 a month to run the shelter.
It is currently full with 80 cats, but the centre told the BBC that there is also a waiting list of 130 people who are having to give up their pets.
Davies said: “If your cat is older and perhaps has a health condition, insurance for that and covering vet costs can also be expensive”.
“So we are finding that a lot of people are looking to us to surrender their animal because they can no longer afford to take care of it,” she said.
“We have unfortunately had quite a few abandonments at the centre, in terms of kittens left in cardboard boxes, cats left in carrier bags and things like that.”
Staff also believe an increase in the number of people breeding cats may also be pushing up the number of rescues.
Davies advised anyone struggling to talk to the RSPCA to see if they can help, such as with pet food provision or by treating cats at its own vet clinic.
