There are numerous and various charities that you can support or that can support you.
Firstly there are your local cat sanctuaries, the local dog and cat shelter etc. These can easily be found in local press, or local telephone directories. some of them will also have a web presence,so a simple search will find charities in your area.
Then there are the national charities.
Probably the best known charity is the Peoples Dispensary for Sick Animals (PDSA), this charity is best known for offering reduced price or free veterinary treatment for people who cannot afford such treatments themselves.
Next consider the Blue Cross, they cover most of the country. They often have animals of all sorts that need a home.
The Cats Protection organisation is responsible for rehousing tens of thousands of cats.
Not everybody lives in a comfortable environment and Paws for Kids is there to help children and their pets who may be suffering domestic violence.