There are no special qualifications for conducting the HGV medical test. Any doctor registered in the UK can be utilised. That means you can go to your NHS GP or a private physician in your local area. But keep in mind that both options will cost you and the doctor you choose must be able to perform the medical test and the vision test. Both options have pros and cons:
Your GP will perform the HGV medical but will charge for their time, often very high amounts. Whilst you may be more comfortable using your GP and they will be very close to where you live, they will often charge very high amounts for their time, and will not be used to filling out the D4 form. This may lead to hold-ups at the DVLA as they request clarification from your GP due to unclear answers. Your GP may also be very busy, causing significant delay in getting your assessment booked.
Private Doctors have shorter waiting times and more flexible scheduling options. They are often far cheaper than an examination by your GP and they do this day-in, day-out meaning they are efficient and know how to answer the form in a way the DVLA will understand. Specialised HGV would always recommend this option as it is often cheaper, quicker, and with a greater chance of being filled out correctly.