Yes. The fees are typically £40k per year. They are said to be capable of getting a below average intelligence pupil into Oxford/Cambridge through extensive tutoring and support. Boris Johnson is a case in point.

In the UK, we have state schools and private schools. The seven 'public schools' are elite independent private schools. In Victorian times, before state education existed, the public schools were those open to all members of the public wherever they lived, whereas most schools were only open to church members or local residents. The public schools were granted independence from the church and crown by an act of parliament, which enabled them to develop to what they are today.