Staycation

Maybe try looking at farm holidays too. A lot of them have been busy erecting tents and teepees on their land for this summer. The kids could "play" with the animals and you could get fresh produce too.

I don't know about availability, but at this place you are near foodie heaven Melton Mowbray and the National Space Centre, which makes a lovely visit for the all of the family
www.eyekettlebylakes.com/

I would look at somewhat lesser known parts of the country. Although as a family we have our own camping gear, I have stayed with friends in comfortable lodges in country parks. Because of finances, we have gone to places, for instance in the Midlands, where the facilities are good, but are cheaper than conventional 'holiday destinations'.

We are taking our children and grandchildren away we are going to TLH in Torquay a large site with 4 hotels and all the entertainment activities and pools that can amuse the children
Cost wise we have found it much cheaper to use these hotels than self catering where caravans ect can cost a bomb plus the cost of food on top
We have booked 6 nights half board for 5 adults and 3 children for around 2k
They often have free child places in the holidays

Have a look at the Haven sites. They have two price structures. Stay and Play lets you use all the facilities and is full price. Stay Only lets you use the takeaways but nothing else and is substantially cheaper. We use it as, although the Haven camps, are big and your view will probably be another caravan, they're great if you just need a base and go out every day.