I've not walked it so can't comment on specifics but if you can't find anyone to pick you up at the other end (taxis will do this often) then obviously you're limited to either there-and-back walks or trying to find loops which will include the Way's path and, necessarily, whatever footpaths/roads you can find to get you home.
Trouble with loops is that you could end up walking 3x the distance for each leg, limiting how much of the Way you manage to a few miles per trip, which at 220 miles, could take you a long time. If you can find a walking partner to go with you then you can do what I've done before which is both drive to the end point in 2 cars, leave one car and drive to the start, leave the car, walk to the end and drive back to the start. Sounds lengthy but given the distances one can walk in a day, it's not.
A good place to start is Bing Maps which you can switch to Ordnance Survey mode. You're gonna need to work out each leg individually and only some serious map time is going to do that I would have thought.