We do not have 'high school' in England. We have secondary school which ends at the age of 16 followed by sixth form college for two years and then university. At secondary school or college age you are a minor and normally will live with your parents although some people do live with other family members. You are entitled to use tax-payer funded schooling in the district where they live.
If your plan was to come to England alone, you would have to attend a private boarding school. This is not cheap but they do take many international students. It is a great way to prepare for UK university.