If you want woodlands, the New Forest might be a good idea. There aren't any proper, ancient, wild forests in the UK anymore, unfortunately, but the New Forest has trees in it, at least. I've been to the Lake District once, years ago, but I can't remember much about it. Can't even remember where we stayed... To be honest I think Snowdonia in north Wales is nicer (sorry, Cumbria).
If you're going to Highclere Castle (and the New Forest), you'd be a fool to miss Salisbury and Stonehenge. It's right there, you know? If you do feel like visiting a city, Bath is very nice. The Roman baths are definitely worth a visit. Portsmouth is good if you're into naval history.
This should be your primary source for prehistoric sites in England. There are some great prehistoric sites in Scotland too *cough* Skara Brae *cough*, but that might be a bit out of your way. I was actually at Maeshowe and Stenness a couple of weeks ago, as it happens...
Cornwall is... rainy. We used to go there every year when we were kids, and it always poured down the whole time. The sea is always freezing cold, it's usually too windy to enjoy the beaches, you can drive for miles without any sign of civilisation. A good place to go camping and escape from the world, I suppose, but I feel like I've had my fill of it for a lifetime... Tintagel Castle is kind of cool, and I remember enjoying Goonhilly Earth Station. Just make sure you've got a good raincoat.