This may seem like a silly question, have you asked your new landlord whether or not you will be allowed to have cats?

Most of the time, the tenancy agreement states no pets... but more often than not, the landlord will accept small animals and cats (providing you keep the animal flea-free and any damage done is repaired at your cost).

I currently live in a privately rented home and my tenancy agreement states no pets... although, I have two rats and have permission to adopt two cats (providing they are flea-free and damage done is repaired at my cost).

You can't lose anything by asking! Good luck...