As a kid in the 50's and early 60's, a trip to the city centre was not complete unless you could mither your parents to stop off for a look at Wiles. I nearly always won. They rarely bought me anything, except for Christmas. It was enough to spend half an hour just looking around the basement where most of the good stuff was kept. Those fond memories have stuck with me and always will. It was an amazing place and so was Lewis' Arcade. Sadly missed. There are some old pics on Machester City Council website when it was a Chemist and another as a toy shop around the same time when your picture was taken. Hope you can find more.
Here is a link to one of the pics showing Wiles on the left of the entrance to Lewis's Arcade Market Street entrance.http://images.manchester.gov.uk/web/objects/common/webmedia.php?irn=1750&reftable=ecatalogue&refirn=67565
Laurs I think you may have given the location of H. Wiles toy shop wrongly.The Triangle Shopping Centre is on Exchange Square.The location of Wiles was on Market Street and it also had an entrance on Mosley Street. The main windows were situated in Lewis' Arcade.Hope this helps.