Cheapest Boarding School in the UK?

There's a reason why boarding schools are expensive. Not just the cost of the accommodation and meals, but also the round-the-clock security and care, on top of the private education of course. There is no chance whatsoever that you can find anything for the sort of money you mention. In fact, you'll be hard-pushed to find a school that only charges that little PER TERM, and there are three terms to a year, plus all the other fees and extras on top! Or looking at it another way, you probably couldn't find a private DAY school for that sort of money, and certainly not a boarding one.

Skip it simple.
STAY home and get educated locally.
No such thing as inexpensive boarding school except juvenile corrections lock up