The best - and most numerous - mountains are in the Lake District. There are a lot of 'camping barns', camp-sites, and I guess caravan parks (though don't know for sure).
The 'touristy' areas - Windermere, Langdale, Grasmere - will be very busy.
The best, and quietest area is the North West corner, Keswick being the major town. But not far from there are Buttermere, Crummock Water and Loweswater.
We stayed several times at a cottage at Rannerdale Farm, on the shore of Crummock water. The farm hire rowing boats, and the views from the middle of the lake, totally surrounded by Fells, is paradise!
There used to be a 'camping barn' at Buttermere.
If you want BIGGER mountains, Scotland is better. Snowdonia and all of North Wales is also super.
www.buttermere-lorton.com/self_catering/rannerdale.htm
www.sallyscottages.co.uk/rannerdale-close
melbreakcommunities.wordpress.com/services/commercial/accommodation-self-catering/
Let me know what sort of surroundings etc, you want, and I'll advise further if I can.