I backpacked the SWCP Exmouth to Poole section in late May 2012.
The typical prices then was £10 for a one man backpacker tent. Range £4 - £14.
Cheap sites:
Exmouth, Pratthayes Farm £4
Axmouth, Axmouth C/S £5
Langton Maltravers, Tom's Field £5
All these are full service sites.
The NT St Gabriels Campsite was £2. Water tap only - no toilets.
Prices are considerably higher in high season - June thru mid September.
South coast prices are always much higher than those in the north. Double would be a good working guide. - This applies to B&Bs (and beer) as well. Mountain huts don't exist and any independent hostels charge more than the YHA.
Wild camping is (just) possible but requires great care - the NT has a blanket ban, and they own all the coast which isn't built on or is a caravan park!
It may be grim up north, but rambling is a lot easier and cheaper!!