In England, you must by law wear a face covering on public transport and in shops and supermarkets as of 24 July 2020.
The Government guidance suggests there is no requirement for evidence for exemption. It should be sufficient for someone to declare that they are eligible for an exemption direct with the person questioning them (e.g. bus driver).
Practices are therefore not required to provide letters of support for those who fall under the list of exemptions, or to those who do not fall under the list of exemptions.