You can apply for a Blue Badge through your local council.
Citizens Advice provides more information in the link below
In order to apply for a Blue Badge you may be asked to provide evidence from your health records. This is easily accessible using the NHS App. Please use this link to find out more about accessing your health records online.
If you would still like a specific letter written and signed by the doctor outlining your health condition then this does not come under NHS work and would be counted as private work which is chargeable at the doctor’s discretion. This is not specifically required for renewing or applying for a Blue Badge and we strongly suggest that patients use the NHS App to avoid this.