>>528559In snowdonia the very northermost tip is pretty quiet and still very mountainy. I like this area a lot and have camped there loads. once you get south to the a5 round ogwyn it's busy, but north of carned llewelyn isn't anything like as popular as the glyders or snowdon massif. Then below snowdon it gets quiet again, quieter the further south you go, but less mountainous. In fact, anywhere without a mountain or name you've heard of is pretty quiet as the area goes.
The lake district I'm not quite as familiar with, but generally speaking the middle is the busy part and much less so round the edges. Again, if you avoid anything with a big name you'll be much more alone. I'd probably skirt the eastermost edge if it were me in your shoes.
With both areas just avoiding famous names will help a fuck load, but it's all relative. I do wonder that if you're going to be restricted to the less dramatic parts of the better parks you miiiight be better off in the more dramatic parts of the lesser parks. Just a passing thought though, not given it much consideration.