Yes. In that row of three story terraces on the south side, opposite and west of The Windmill. I assume that it's now one of the sporadic shops in that terrace.
I was just testing to see if anyone else remembered Bardsley's when they were also based in Upper North Street, which was for a very long time up until the 1970's. Our Mum used to take us there in school hol's.
Memories:
http://www.mybrightonandhove.org.uk/page_id__5321.aspx