Looking at the building again, it does look like it would have a basement, does this ring any bells? http://www.flickr.com/photos/53761336@N00/4177970983/lightbox/
I think Vic may be right. Does that little sign say Classic where the green doors are? The comments below people arent sure either. Someone mentions the barbers pole which i remember now!!
I think he must have moved across the road at some point to, apparently he used to be in the King Albert Chambers arcade next door to Just Films opposite my old mans place, you can see the red and white pole at the side... http://www.flickr.com/photos/sydpix/6819085568/lightbox/
That's the entrance ! And your recollection of Father and Son, is also correct, because Steve Rowe was the Son !, his Dad must of retired before I started going.(hence the wig fitting). I went to get my haircut on a return to Hull, when it moved across the street only to discover he didn't cut hair anymore and had taken up piercing. I asked the girl ( turned out to be his daughter) to get him anyway. When he came out of his "room". He laughed and invited me in, to look at his new business venture. He also showed me photos of his latest skill of piercing any part of the human body imaginable. Probably illegal nowadays .
I have to say I don't remember any basement near the mail building. I went to the mail building a lot as a mate I played golf with worked there, and I sure I would have remembered it.