Each affiliated cat club has an officer who deals with welfare matters: they maintain lists of older or rescued cats that need homes together with lists of people who are willing to offer homes to such cats.
All clubs will offer advice and try to help if a pedigree cat needs rescuing or re-homing and some also have facilities to take cats in while awaiting new homes.
If you have to re-home a pedigree cat you should always contact the breeder first if this is possible: most breeders, if they cannot take the cat back themselves at that time, will do all they can to help to re-home the cat. If it is not possible to contact the breeder, or the breeder is unable to help, the next point of contact should be the appropriate specialist breed club, or an all-breed club in your area: the contact telephone numbers, and email addresses if available, are listed on club websites. Do not worry if the contact number for the breed club is not local: many larger breed clubs have regional officers who they can contact or put you in touch with, while the smaller clubs will often know somebody in your area who can help.