The headmaster of Carmel College, which is Europe's only Jewish boarding school, wrote to parents of its 200 students on Friday to inform them that "the college will no longer operate after the end of this academic year".
Philip Skelker said the unexpected move was forced on governors by a rapid decline in numbers at the Oxfordshire-based school over recent years.
Dame Shirley Porter, the former leader of Westminster City Council, is one of the governors of the school which has produced many high-flying former pupils including the Conservative MP Spencer Batiste.
The college was the first in Britain to charge more than pounds 10,000 a year in fees and in 1990 it topped the list of the 20 most expensive boarding schools in the country.
Parents said they were furious to get such short notice of the closure and feared many children would have to retake a year because of the difficulty of finding schools offering equivalent GCSE and A-level courses.
Toby Tenenbaum, an 18-year-old pupil, said: "I was appointed head boy last Tuesday by the headmaster, and then on Saturday I got a letter saying that the school was to close at the end of next term.
"I am extremely upset by the news and am very worried about finding a new place to do my A-levels."
Rabbi Jeremy Lawrence, who teaches in the school's Jewish Studies department, said: "The news was extremely sudden and extremely shocking.
"Carmel was more than just a school. It was very much a community and a way of life."
Beverley Bond, whose son is in the school's lower sixth, said: "I'm furious. If we'd known at the beginning of the year, it would have been much easier to move our children before they started on their A-levels."
The school was founded in 1948 by a Rabbi, Dr Kopul Rosen. A large proportion of the school's pupils have their fees paid under the assisted place scheme.