After a bit of digging I've found the relevant government guidance on the use of face coverings in primary healthcare settings. It's very brief.
www.gov.uk/government/publications/wuhan-novel-coronavirus-infection-prevention-and-control/new-recommendations-for-primary-and-community-health-care-providers-in-england
Unlike the use of face coverings in shops, public transport and other indoor spaces, GP surgeries and other health care settings are not covered by legislation - this is guidance:
- providers of primary and community health services should ensure that measures are in place so that all settings are, where practicable, COVID-secure, using social distancing, optimal hand hygiene, frequent surface decontamination, ventilation and other measures where appropriate
- where a setting cannot be delivered as COVID-19 secure through all other means, a local assessment may conclude that primary and community healthcare staff (both in clinical and non-clinical roles), when not otherwise required to use personal protective equipment, should wear a face mask; worn to prevent the spread of infection from the wearer*
- where a COVID-19 secure environment cannot be maintained, patients and members of the public entering primary and community healthcare premises should be advised to use face coverings in line with government advice
So the government advises that they should do all the other stuff to make their setting 'covid-secure' and if that can't be maintained they should advise patients to wear a face covering in line with government advice - which, as we all know, includes exemptions as well as a request that people be mindful and respectful of the circumstances in which someone may be unable to wear a face covering.
This is guidance, not the law, so GP surgeries don't have to follow this. They can come up with whatever policy they like as long as it complies with all other existing laws, including the Equality Act.
It doesn't look good for a GP surgery to be ignoring both government covid advice and the Equality Act.