>>2085492Brecon in Wales is quite empty if you can dodge all the military training areas. Snowdonia is very pretty but more touristy.
North Scotland is peak /out/.
Norfolk broads is worth the visit even if it's just to laugh at stupid chavs crashing boats while drunk. I view Norfolk as the Florida/Alabama of the UK.
The New Forest like I posted earlier has horses, they're not wild or anything but it's a neat thing to see given the low number of wild animals in the UK in general. Worth it for the day trip but like another Anon said, no wild camping (there are some camp sites that are just fields with trees though so you might be okay with that).
Also I would highly recommend a kayak if you want to go /out/ in Britain, we have a stupid high population density in England (Scotland and Wales don't apply for this) so it can be hard to get away from people sometimes.
Also the Isle of Wight is very pretty and has red squirrels, same issues as with England (pop density) but it's worth visiting once.
Other than that just stay away from cities and you'll be fine, especially Birmingham, London, Manchester etc.