Hoop is another good app for finding what's on near you (mixture of free and paid events)
West Midlands here - we'll be spending a lot of time at the library, which is putting on some free special events across the summer. Park Lives is near us for free active stuff in parks - might also be near you, it's nationwide. Museums are usually free or small charge, check before you go. Check local papers/online for events - our local council website has a "what's on" page. Children's centres may have a couple of things on appropriate for your youngest two.
Do "cinema" at home - scour the TV listings for a film you want to see, or charity shop DVDs, or Netflix, whatever you have, get some popping corn (or microwave popcorn, but popping corn is cheaper) and make popcorn and all curl up in the living room with the lights off.
Make dens - indoors with blankets and cushions, in the park with branches etc (don't take them off the trees, just use stuff already loose)
Bake! And then take the goodies you make on a picnic.
It doesn't need to be all action, all singing, all dancing. Your kids will just remember having fun, and that you were there - not that everything was free.