Where am I able to do my laundry in the Peak District, if my accommodation doesn't provide laundry services?
There appears to be no self-service laundromats or laundrettes in the Peak District proper any more. Instead there are only laundry services in Bakewell (GBP 9 per load) or Tideswell (GBP 4 per kilogram), both of which are decidedly more expensive than doing laundry yourself but correspondingly more convenient.
However there are a couple of options just outside the Peak District itself. There is a laundrette in Buxton if you are in the northern half and one in Matlock if you're staying further south. These are both easily accessible by public transport from various parts in the Peak District depending upon your location.
I have traveled to the UK before and found coin operate launderettes as well as service laundries thin on the ground. Many local people use them for large items like blankets of bed quilts that won't fit into their washing machine. At a B&B in Aviemore I used their laundry but was asked not to use the tumble dryer as it cost them money to use. The laundry area was humid and damp with clothes hung everywhere but nothing drying. So I used the tumble dryer. I gave them 20 pounds and they still whinged and moaned that I'd used the tumble dryer. I refuse to wear damp cloths just to save a tight B&B owner a few quid.