The Royal College of St Peter usually referred to as Westminster College has been here (in the grounds of Westminster Abbey) since the 12th century.
With a role of 750 this is one of the most prestigious and expensive schools in the UK, costing nearly £10,000 a term for a boarder. Apparently this pays off as the school has the highest Oxbridge entry rate, at 49.9% between 2002 - 2007.