Never heard of any of them, I don't think they're really 'public' schools, they're rather smaller ones, I'd imagine.
I think you'd be better off going to one of the bigger public schools; Marlborough, Millfield, Bryanston, Kings Taunton, Queens Taunton, Taunton, Canford, Clayesmore, Repton, Rugby, Stowe, Sherborne (Boys & Girls), Cheltenham, Clifton etc.
That is total and utter balls about them 'not putting you in a house', as 9 times/10 they will. We have some German and French students over for a term at my school and they're in a house. It totally depends on the schools' system, at my school you live/eat etc. In the house, day pupils too...So, if you're not in a house, it's terribly silly you coming. That happens in lots of other schools too, so don't be put off by that comment.
I think it'd be a fab experience, you'd be able to experience the way of 'english life' and have a fab old time. Def. Do it!