Schools and schooling are a little different in the UK than in the U.S.
For example (as has been stated before in other posts) what the U.S. would call "private schools" are in the UK public schools. This rather odd situation came about long ago when the private schools there were mostly run by religious organizations. Later, anyone who could afford the tuition fees were allowed to go to school there, even if not affiliated with that particular religion. That is, the "public" could now attend. The school was still private.
Speaking of religion, in the "true" (by the American definition) public schools, there is not in the UK separation of church and state: Religious things - including actual prayer - are allowed in the classroom there. At least this is what I read. I am depending on my readers to correct this if wrong. This has not been allowed in U.S. since the 1950s of course. So elevated is our thinking.
If this situation has changed, or is changing, in the UK, I would appreciate your input.
In the U.S., the trend is now toward private schools (in the true sense of the word "private") and to home-schooling of children. This has been the case for many years now. Public schools are still by far the most prevalent. Private schools are mostly run by religious organizations. Prayer and religious teaching are allowed in private schools (and of course in home schools.) Prayer and religious instruction (other than the teaching of comparative religions as an actual class) is not allowed in the U.S. in public schools any more.
Many changes have been effected in public schools in the U.S. in the past decade. Uniforms are becoming more and more the norm in many high schools. This to fight gang "colors" mainly, but also is an attempt to instill a little pride in the students, by being dressed neatly and non-competitively. In all public schools one will usually find official rules against bringing drugs (even aspirin) to school, or weapons of any kind. Inner city schools will find metal detectors and city police patrolling the hallways commonplace. Certain constitutional rights have been suspended for students in public schools, primarily search and seizure and privacy of personal papers and belongings.
In the U.S., high schools are often referred to as prep schools, meaning preparation for college after high school graduation. But in the UK, I believe prep refers to a more elementary school level.