All service stations which are signposted from the motorway network are required to provide shower and washing facilities for HGV drivers. Other service stations are not required to but are encouraged to do so. The regulations don't state that the shower must be free, but this is generally assumed to be the case.
Service stations which were last refurbished prior to 2013 are not bound by this agreement, but the overwhelming majority do anyway. This website lists 'Showers' as a facility when you look up a service area. There is also the opportunity to leave public feedback on the quality.
The facilities are expected to be in clean condition and good working order. The quality varies, due to a mixture of customer misuse and bad management. To tackle this, different services have tried a number of measures, such as requiring you to ask staff for a key to the shower.
One of the first service areas to provide showers was Forton, in 1965. A report in 1983 suggested that only eight motorway service areas were able to provide showers for drivers. They are now available at almost all of them. In general, the quality has improved over what it used to be in the 2000s, probably because professional drivers have become vocal complainants when expected to use dirty facilities.
Complaints about shower facilities at service areas should be directed to the operator.