Thanks for all the replies!
(Yes we still have Butlins but think they only have 3 sites now). We have often done the weekend away holiday offers from the Sun newspaper, for £9.50 upwards per person, makes for a cheap break as there are 5 of us, but you normally can only get off season dates, and windy wet rainy caravan parks are not my idea of fun lol.
Not ENTIRELY sure this is something we will miss anyway with so much to see and do

On our summer road trip, we drove past a few water park type places that were a bit like what you're after. When we googled about them, they weren't especially cheap though. Out in OH/IN

Yes, KOA are more focused on RV's/Travel Trailers, although all of the ones that we have used have had a few cabins as well - ranging from 2-3 on smaller sites, to 10-12 on the bigger ones we've been to. They're not really holiday camps though - more like caravan sites with facilities. Most have a pool, playground, game room, fire pit etc, and they will arrange some very limited activities - outdoor movies some evenings, maybe a craft activity or smores round the fire. Some of them serve surprisingly good breakfasts - the breakfast burrito with red chilli sauce in N Albuquerque KOA was fantastic!! We use them primarily because a) they are generally well kept, and b) there are always other kids around for mine to go and play with.

I don't know of any holiday camps as such, apart from the already mentioned Great Wolf Lodge (which we haven't been to, but a lot of friends have) or the floating camps aka cruises - we've done Carnival and Royal Caribbean, which are OK, but not really my thing...but the family enjoy them. Are Disney cheap in that genre - I always assumed they'd be pricey? We did go to Atlantis Bahamas a couple of years back - that's sort of holiday campish, and was great fun, but again, not exactly a cheap getaway. I've been looking at some of the Beaches resorts, particularly the one in Turks and Caicos, which gets great reviews, but I'm balking a bit at the price tag for spring break...

Ah, just remembered another one - google Jellystone Parks near you - I think its a national franchise. There is one near us that has water slides, lots of kid activities, cabins and tent/RV camping. We went once and the kids loved it. I managed to find other places to go after that until some friends arranged a multi family trip there. Again, the kids all had a blast, but funnily enough, none of the parents suggested it for subsequent weekends away............

Center Parcs did consider the US market when it was a "complete" company back in 2001, but their market research told them that it would just not appeal to Americans.

We've looked at KOA, but it is SO basic to the point of being painful. I loathe camping and this is REAL camping (bears and all). A lot of the hotels are almost too luxurious - we don't want to be pampered for a week.

The best we've come across are Embassy Suites and then things "to do" in the area. Unfortunately, that means the bl**dy car has to come along as well - the great appeal of CP for us was driving up on a Friday and then not touching the car for 7 days..... Bliss.

We had quite a few camping holidays with the kids through Haven/Eurocamp before coming out here. Haven't found anything similar since being here (7 years now) but did think the Jellystone ones looked the closest match. Accommodations didn't look nowhere near as nice as the Eurocamp ones. We just wait until our annual trip to the UK and do a side trip from there, had a lovely week in the South of France with Eurocamp this year

We did stay in a cabin in Cape Cod on a campsite that was perfectly fine, they had a bit of entertainment and swimming pool on site but it was still basic compared with the sites in Europe. On the plus side here, house rentals can be cheap but you have to provide your own entertainment

We stopped at the Jellystone Park in Arkansas long ago when we made our trips across country to see relatives on the east coast. Think there were just a few of them back then. I can't believe they have spread so far and wide (even into Canada) since.

Though I see only one (near SF) in all of California, so the OP may have to drive a bit to find one. No fun for adults there, IIRC, but the kids enjoyed themselves.

We're planning on the same next year when we head back to the UK. 2 weeks with The Family, then take a week to head down to Pierre-et-Vacances at Marina Baie des Anges (near Cannes). For July/August, we've had to book already as things are starting to fill up....

We've done Keycamp/Eurocamp/SiBlu/CP in the past - fantastic holidays each one.

We booked really early too as some of the family from England came with us. Such good holidays, the parks are fantastic, we stayed at Les Sablons, near Beziers.

In this area, there are several "resorts" that seem to be popular with families, especially from California. Most of the resorts are based by lakes. Most of them have switched to their winter, snow based, activities by now though.
http://www.elklakeresort.net
http://www.seventhmountain.com