It would still have been The Princes cinema when this photo was taken.
My continued searching paid off, and I managed to find out a few more bits of information regarding the history of this building. Apparently it had another slight name change in 1937 when Francis Bertram took over the cinema, and renamed it The New Princes. CA & HA Sellers took over the auditorium in 1940, and in the late 60's Charles Crayford became the new owner, under the company name of Craydem Cinemas Ltd. It was Crayford who changed the name to The Rio, chosen to compliment the other cinema he owned - The Rio on Canvey Island. Andy Whyatt took the cinema over in 1979, and is possibly still in charge today. Meaning this cinema has remained as an independent for the whole 80 years!
I also found this picture, taken around the time that Andy Whyatt took charge:
Taken from almost the same spot as I took mine on Friday....