If you have found an injured or otherwise distressed animal:
RSPCA – Injured Wildlife Advice NB: The RSPCA will usually only arrange to collect an animal if you can still see it and confirm it’s whereabouts. They also give advice on taking found animals to vets on the linked page.
There are LOTS of wildlife rescue centers out there! Search for “wildlife rescue” plus the name of your local area and plenty of options (too many to list here) will appear, hopefully one of which can help your patient. I’ve only listed national organisations or those I’ve dealt with myself here.
If you are hoping to re-home an adopted pet:
RSPCA – Find A Pet (all pet types)
Just For Dogs (Derbyshire area)
The Pipsqueakery (USA) (hamsters) These guys have an amazing social media presence if you would like to see some cute hamster photos!
Support Adoption For Pets – Find a Pet (all pet types) SAFP have small animal adoption centers in Pets at Home as they will take returned and unsold pets. This is where both of my hamsters came from.