You can't go wrong with Biology. Chemistry and Maths are the other things you need to become a vet, I'm not sure how far in line that is with your choice of career.
I envy you, I have just done my A-Levels, and I wish I had a goal, a purpose to drive towards. It will help you, and if you put the effort in, it will pay off.
Bio, Chem and Maths are probably not essential for the role, but are useful, and will open up other doors beyond the RSPCA if you choose to explore them. But it is hard work. Make sure you choose subjects you will enjoy, that is crucial.
click here an Association for Colleges gives details of all colleges providing animal care etc courses. Most of them now run degree couses rather than diplomas so 3 good A's would seem likely. You can search for courses from the site.