The English school system in the 50s was based on public (i.e private fee paying schools), grammar schools (which were entered via an exam) and secondary modern schools where everyone else went. Schools like Eton and Rugby were public (private) and were fee paying but they also offered scholarships to anyone who could pass the entrance exam.

I'm not totally sure about the navy question but I think the Royal Navy had a minimum service term of 20 years (or at least they did in the 1980s). Once you'd passed the 6 weeks induction you were in until you retired or you bought your way out i.e. you paid a fee to leave.

Hope this helps.