try this link for some ideas. You can put in min and max distance, press search and you'll get a list of all the trails in the UK.
http://www.ldwa.org.uk/ldp/members/search_by_path.phpThe ODP is a good suggestion - It can be camped almost every night, although the central section can be a bit awkward for tenting. You could always treat yourself to a B&B or two! There's only the one hostel at Knighton (or Kington - I always get confused between the two places). There is also a fairly new bunkhouse attached to the pub in Bodfari? at the end of the penultimate stage if walking North.
Although you will never have villages as lunch stops, it does split nicely into stages with each one ending at some sort of settlement.
It is also one of the best walks you'll ever do
Failing that, you could walk one end of the Pennine Way or do the Coast to Coast.
As a left field suggestion, what about the North Downs Way? There's two hostels on it at Tanners Hatch and Canterbury, but apart from that not much else. It is quiet enough that if you pitched sensibly and carefully you could probably just about get away with wild camping - it is a surprisingly quiet trail. It does tick most of your other boxes though, and comes in at around 130 miles. Not high but it has its share of ups and downs - box hill is a fun climb