It can be a bit of a postcode lottery for NHS audiology. Some areas seem to be able to provide bluetooth aids, some don't.
I did go private, realising it would cost me quite a lot, but am very happy with my hearing aids and know that I can phone them at any time and be seen within a day or two. No further costs for the next 5 years - all follow ups etc included. Also, I know I will see my "own" audiologist, rather than a parade of different ones at each appointment.
Having said that, the NHS aids can be perfect for many people, although the initial waiting list can be long.