On some national trails there are organisations that do this sort of thing. They will transport your luggage along the trail - from hotel to hotel (or Bed & Breakfast, more likely). I explored this option when I tried to walk the Two Moors Way (Dartmoor and Exmoor).So how can one do that without a tour organizer? Is there a means of sending luggage ahead? (Could I call a taxi and pay him to run it to the next B&B?) And how about picking those B&B's in the first place?
Maybe your best bet is to choose to walk a small part of one of the national trails. See general info about them here: http://www.nationaltrail.co.uk/
And look at more detailed info from here: http://www.nationaltrail.co.uk/text.asp?PageId=2
Then you can choose a trail that interests you - for example, as you mentioned cliffs before, the South West Coast Path might be good - and then contact the addresses/email etc. that are given to get further information about that trail to ask them if the luggage carrying thing is available on parts of the trail.
That's all I can think of for now, anyhow.