BMA Guidance is:
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 (eg 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.
Some transport providers are providing evidence of exemptions themselves, see for example this information from First Bus and Arriva.
Patients can download their own exemptions: