I've done a (very) quick Google, they're not obliged to follow the curriculum, or the requirements such as teaching an hour of RE a week that state schools have to follow.My daughter is choosing her GCSE options right now, and it seems to be exactly the same as state schools. Must have a language, must do science, maths, english etc.
Types of school
Types of school and how they're run - community schools, academies, free schools, faith schools, state boarding schools
www.gov.uk
I gather most of them broadly have the same requirements for GCSE subjects just because it turns out that teaching children English, Maths and Science is a good idea.