I think the key to a fun walk in the UK with children is old clothes, good wellies and warm coats. So that they are comfortable and you're not constantly telling them to avoid the mud. If it's a cold day the kids wear tights under their trousers and that goes for my son too. He does love his sister's pink cast offs! And we are a two pairs of wellies family, so that if they are completely sodden and not had time to dry out there is another pair to wear on the next day's walk.
We carry a bottle of water and a treat to refresh and motivate with all that healthy outdoorsy air. Sometimes the treat is healthy, but, sometimes I'm afraid it's not. Sometimes it's a combination of the drink and the treat in the form of "special juice" as we call those juice drinks that I don't allow the kids at any other time.
The other rule is the kids get to do what they like (as long as they are safe obviously). We go at their speed, we stop and look for hours it seems at a fallen tree stump or muddy ditch. If they want to twirl sticks around, "great"; climb trees, or more scarily jump out of them, "wonderful"; make mud pies, "that's fine"; dig goo out of tree stumps, "lovely!"
In the car we leave a change of socks, and if it is a really rotten day spare trousers, and often another treat to keep them quiet on the drive home. We always have a bottle of water in the boot of the car for the dogs, this also usually gets used to rinse hands.
Along with the exercise and the blowing away of the cobwebs, walks are an inspiration for craft ideas. Today Una wants to make hedgehogs when we get home. (I'll post the results later.) The children make daisy chains, leaf sculptures and will take a liking to a leaf or stick that is then carried with us for the rest of the walk. There is blackberry picking in the autumn, we also have plums, damsons, apples and sloes on our regular walk. And this year I've made elderflower cordial with the children and am attempting sparkling elderflower wine for mummy and daddy.