Most medical examinations required by third parties (eg HGV licence, pre-employment, sporting activity, insurance, etc) are not part of the NHS services. There is normally a charge for these medicals. You will be advised of these at the time of making your appointment.
Please see the document below for some of the services provided
Medical Certificates, Reports & Examination Fees
You do not require a doctor's certificate for any illness lasting six days or less. Your employer, however, may require you to complete a 'self-certificate' which you can obtain either from your employer or local DSS office (it is not obligatory to see a doctor for this). After the seventh day you will need a doctor's certificate and you need to be seen by your doctor.
For a private doctor's sick note the fee charged is £32