The Exmoor holiday rentals listed on this page all have a power shower, so that by booking one of these, you can continue to enjoy your daily invigorating scrub.
Please read the description of the shower, most power showers would be standalone cubicles, either single or double.
Good water pressure or a pump is needed to maintain the high pressure required to produce a strong stream of water. That may not be available in all rural areas. Some properties may rely on their own borehole.
Towels are supplied at holiday rentals as they would be at a hotel. The only towels that you need to bring are those for the beach or a swimming pool.