have you looked at gullivers?
sure ive seen an offer for family of 4 £49, family of 5 £59.
If you dont have the stuff to camp have you considered a youth hostel?
Bunk rooms, some have an en suite, some you share facilities (which are normally spotless), and then most have family / games rooms, with games and books etc and a decent kitchen, so you can cook normally, make yourself a picnic etc and dont have to pay extortionate prices to eat out.
Also you have access to a fridge and a freezer etc.
Most have gardens
and the majority are in nice places with free walks etc on your door step.
My children absolutely love a youth hostel break.
We got 2 nights in scarborough on booking.com for £80 during may half term.
a room, which shared facilities (including a fully equipped kitchen) with just 1 other room.
One day we did a very long walk along the coastal path, then took the bus back (my kids were £1, i was £3, we took our own picnic lunch, which we ate on a beach, i made breakfast in the kitchen in our accomodation, and we did have fish n chips and a doughnut for tea at the beach, but we could have cooked our dinner as normal in our accomodation) My only expenses that day was an ice cream, fish n chips, £5 bus fare, and £40 for the room for the night.
Also look at planet offers for half price days out, which currently include flamingo land (Under £100 for a family of 4) and alpamere water park for £35 for 4 people