Face coverings are now mandatory in many public places. Government advice says you should wear a face covering in enclosed spaces, such as public transport, shops, supermarkets and hospitals. You are also strongly encouraged to wear a face covering in other enclosed public spaces where social distancing may be difficult and where you come into contact with people you do not normally meet.
There is no requirement for an individual to prove that they have a valid case for exemption if they cannot wear a face covering. Given this GPs are not expected to provide a letter of exemption.
If you would feel more comfortable showing something that says you do not have to wear a face covering general template cards are available to download or print below. This is a personal choice, and is not necessary in law, saying that you are exempt is good enough.