Someone who is trained to care for injured wild animals is usually called a wildlife rehabilitator, wildlife rescue centre, or wildlife rehabilitation centre. Rules and permits differ between countries, so in United Kingdom you should contact an authorised rescue centre, wildlife authority or veterinarian before trying to care for the bird yourself. Some centres accept almost every species, while others only accept certain species. With a bit of luck you can get advice by phone without transporting the animal, so call first.
Reliable links / contact lists for United Kingdom:
HelpWildlife – wildlife rescue directory: https://www.helpwildlife.co.uk/
If a reliable rescue list is missing, or if one of the links is outdated, please let me know and I will update this page. P.S. remember that many people who help wildlife are volunteers doing this work alongside another job.