The final day's walk to Minehead lays along the Somerset Coastal Path. Logistics Dartmoor is about the nearest that England gets to wilderness. It's a vast moorland plateau, largely uninhabited and uncultivated. Eventually you'll come out at a road somewhere. Backpacking is an option but camping is more difficult than you might think and there are few opportunities for camping wild, even on Dartmoor.
Transport needs careful planning here and there, particularly at weekends and on public holidays.
Call in at the local tourist information office wherever you are staying. On the moors the route, though rarely marked, is always pretty obvious. In more pastoral country, particularly mid-Devon, the TMW is very well waymarked but local paths can be all but impossible to follow. I've tried, as far as possible, to align the route away from any such obstacles but circumstances change from year to year and even from month to month. If in doubt stick to the line of the path as marked on the map as far as is practicable.