We spent a week in Bath this May, and used SpeedyWash with very good results. (They are listed in Rick's current guidebook.)
They picked up our laundry at our hotel in the morning, and returned it the same afternoon. They charged Ł20 cash for one large load (which filled a 13-gallon kitchen trash bag). They also gave the option of paying Ł24 via credit card.
I thought it was well worth the money. They were also very friendly and helpful on the phone. Highly recommended!