Things aren't necessarily just between you and your GP. Covid-19 is now a notifiable disease -
https://www.gov.uk/guidance/notifia...sms-how-to-report#list-of-notifiable-diseases
........and has to be reported by law, including your personal details -
https://www.gov.uk/guidance/notifia...s-cov-2-test-results-to-public-health-england
Anyway, I quite like the idea of anti-vaxxers and Covid deniers and free thinking libertarians who think that wearing masks and following Covid rules doesn't apply to them being told, no, you can't come in.
Telling the health authority that you have a notifiable disease is completely different to showing part of your medical history to John, the landlord of the Dog and Duck, part of your medical records.