Update 8/22/20. With the help of Barry Love, who is setting up the real Royal Enfield Museum in Redditch we were able to find it, it is the one labeled Royal House in this picture,
Funny story: in one of my visits to Redditch I mustered the courage to ask a couple of old timers in the street "there used to be a Royal Enfield showroom around here, do you know where it was". They replied "no, we're not from here, we're from Eversham. And they are in India now anyway!". I was literally standing in front of the store when I asked that question!
Update 9/11/21: A spectacular investigation by Simon Taylor indicates the store was actually at 8a Church Green. See details here.