Depending how far you want to walk each day, the Cotswold Way is a very nice 110-mile walk.
This page here has useful information on where the campsites are and if the distances work for you, that might be an option (although possibly slightly too short for 2 weeks?)
In general, camping is a lot more expensive in the south than the north. Since moving down south I've noticed there are far fewer cheap and cheerful campsites than in the north - far too many are big sites catering for families, meaning you're paying for playgrounds and swimming pools you're unlikely to use.
One other option might be to join the
Backpackers Club, which gets you access to their list of unofficial campsites and farms that allow camping along most of the long-distance paths in the UK. That makes camping feasible along almost all of them.