There are absolutely loads of foraged foods if you can co-ordinate things, sort out leisure activities like walks and amusing the children. Not including things you need a permit for:
If you live by the sea: crabbing is a doddle and good fun with kids, razor clams are edible, cockles and whelks obviously. Squat lobsters are incredibly delicious.
Rivers: if you can get signal crayfish, you're doing the ecosystem a favour as they are an introduced species which is knocking out the native crayfish. I've known people collect so many in a day that they just went round to local restaurants and sold them on.
Hedgerows and woods: Elderflowers and elderberries, hawthorn berries, ramsons, mushrooms of course (eek, though, I wouldn't be confident unless a really obvious kind like puffballs), juniper berries, blueberries, wild fruit everywhere, nettles...the list just goes on and on.
You'd have to be very hardy, very time-rich and energetic to get the bulk of your diet from foraged food, not an option for anyone really. However: children need to be walked, we all need more exercise, picking a bit of stuff as an extra is really satisfying, and working out what to do with things improves your cooking skills. There are tons of vitamins in things like elderberry robb or hawthorn syrup. OK it's ridiculous to assume that everyone's going to be interested or bothered or able to do this, but that doesn't stop it being a healthy and satisfying thing to do. (In particular it feels good sticking it to The Man and getting tasty stuff for free.)
When you google foraging, the first hits you get are from people selling their knowledge to the middle classes, or selling their books. The fact is you don't need them: keep googling, look on message boards like this one, pick out the useful bits and you can find the same knowledge for free.