Holkham and Wells are both a long trek to the beach. Wells does have a car park near the beach, but in peak season you usually have to park in the overflow in the town and either walk or catch the little train (which can be busy) to the beach.
If you check the tide table for Holkham and go at high tide then it's a shorter walk along a wooden gangway (10 mins) As the tide goes out then it flows through all these shallow sandy channels which my children love to dam up, and dig in.
Forget the rest Holme is best! It is next to a rspb nature reserve, you park (nice cafe plus eco loos there too) and walk 2 minutes up through pine trees out onto a quiet beautiful white sand beach. I have been to all the beaches mentioned numerous times with little children and you can't beat it.
Thanks all so much for your tips. I'll definitely look at some of the options with the parking right nearby. We're not looking for huge days out on the beach, but an easier park and a couple of hours play would be fantastic!
Wells beach will be much quieter than in high season. We were there in August but still managed to park in the Pinewwods car park so you just walk over the hill / sand dune to the amazing beach. You can rent a beach hut from Pinewoods on a daily basis too (£20 ish). The beach is beautiful - big and sandy.