Jagex have some student internships:
Ok cool thanks. I've seen it. Kings have a internship program as well. I applied for that a few weeks ago.
Also if you have a good portfolio and you feel you have what it takes, some advice a guy in the industry told me (it was for sound tho but I guess it's around the same) is to apply for internship everywhere you want to and don't wait to see if they do internship or not. They almost never post their internships.