In reply to georgiaaharriet:
Upper Eskdale is a good call, especially if you go off piste on The Great Moss and on the southern flank of Esk Pike. The head of Lingcove Beck feels very remote too.
Some of the most challenging navigation that I performed in the Lakes was on the low range of hills south of Eskdale, blundering around on the northern slopes of Yoadcastle with the clouds down in a gale, trying to find an elusive tarn near the summit, which isn't even marked on the 1:25000 map. Lots of false summits and little crags to negotiate before I could pitch my tent.
Another interesting and remote area is the Copeland Forest, the lower hills west of Pillar and Scoat Fell. The Nether Beck valley is lovely as well as being quiet, and the Worm Gill and Bleng valleys are positively deserted - plenty of off piste routes there!
Post edited at 14:22