Book a long way in advance. We booked center parcs this year for the February half term, so a less popular time of year than when it's warmer, but by booking 14 months in advance it was £1200 for 7 nights and not in the most basic lodge. We looked at all of the sites within 4 hours of us, and I'm guessing some areas have different half terms to when we have ours, as the sites further south were significantly cheaper the week we wanted than the ones further north. It's still a lot for a lot of families though.
Likewise we're doing a 4 week mini tour of Europe, we're lucky that both of us can work from anywhere, so will do a couple of days a week throughout the trip and we've booked places with gardens so the kids can have those days just playing as they choose, but we booked a long way in advance so we got the better value accommodation and we can also pay off £50 a month or whatever, none of our trip is over £100 a night and most is under £80 a night for 4 people, apart from the one night in Amsterdam, even the overnight ferry was £162 when we booked it with an outside cabin, but for the same day now it's over £300 and it's still 7 months away.
Another option is the Sun holidays for £9.50 which were released a few days ago, we do a couple of weekends a year for under £100 for the 3 nights, but our biggest bargain was booked 2 days ago which is a week in France in October half term, and was £159 for a 3 bed caravan for 7 nights. If there is nothing left on the Sun's site itself go straight to eurocamp, it's only about £50 more to book with them direct. Other sites may be very different in price but this was in Normandy. It's a huge difference compared to going in peak August dates, but you can still see somewhere new, play on the beach, and for smaller children especially we've always found the shoulder season a better climate than peak anyway.
Travelodge are a great alternative to explore new areas too if you're not a camper and want to see the UK, last year we ended up spending a week in a Travelodge for £180 in August for a 4 person family room, and that was booked fairly last minute, so there are options, but you do need to be creative to keep it on a budget.