Nope, some of the worlds elite Drs donโt necessarily belong to some of the acronyms such as ABHRS/ISHRS/IAHRS, it is by no means any sort of guarantee they are capable of a good Hair Transplant.
What you need to look for is plenty of patient posted reviews, some of the more well known names have been putting out decent/consistent results for many years.
Dr Reddy has recently become forum recommended again, others that you have mentioned do have the occasional miss, but this is true of every single Dr (even the so called elite) If you are adamant about staying in the Uk then just research as many of the top choices as possible.