Here’s an ad for Barker’s Bread from the May 27 1930 edition of the Toronto Daily Star:
Barker’s Bread had just switched locations at the time of this ad, as the 1930 Toronto city directory lists them at 279 Spadina. They remained at 559 Davenport for some time. By 1950, the firm was known as Barker’s Biscuits. The last city directory that they appear in is 1953.
There is an old Torontoist page that provides some information on Barker’s Bread (the link may be stale, though, as the image that was originally included with the page is no longer there).