My DSs went to the Supercamp held at St Swithuns (highly selective public girls school, Winchester) a couple of summers ago. Supercamp merely hire the facilities like you might hire a local school hall for a party. Your DCs certainly don't have to attend the school.
To be perfectly honest, it didn't suit them. They went for I think it was 2 or 3 days for 2 weeks, so perhaps 6 days overall. It was obvious that many of the DCs there knew each other from school and did this EVERY holiday.
I think it was well organised- I'm not criticising Supercamps!- it's just that everything the DCs did seemed to be go, go, go and rather competitive. They're immediately put into teams with names like "Panthers' on arrival and stay with that team, and the teams are run by very enthusiastic young people. A strong 'team spirit' is encouraged. The boys arrived every morning to a hall full of very competitive alpha boys wildly kicking balls around with gusto and giving newcomers a BIT of a cold shoulder, prior to the organised sport- I mean 'activities!- to begin.
I did feel the advertising implied 'Swimming! Quad Biking!' etc but the DSs swam once a week and never saw a quad bike. It cost me 28 and 25 quid per child.
Now, it might be fair to say 'Horses for courses' and Winchester is VERY yummy mummy, thus the Supercamp might reflect this more than your local one.
I originally sent the DSs to the local comp's holiday club the year before, and felt my two, then 5 and 7 spent their entire time in a large school hall watching 14 year olds play on the computer games so I thought Supercamp would be more fun. THIS year just gone I sent the DSs BACK to the local comp which has upped its game considerably- it's 4-11, 11+ now and they choose a couple of organised activities to do, but they can also just sit out and read, draw, watch a movie etc, Much more relaxed. And much cheaper (18 and 15 quid!). Whilst my 2 will never love Holiday Club I think I will be sending them to this one in future.