OK I'll tell you what I know.
I'm told the lady is Hilda Wilkinson (born in Chorlton-cum-hardy, Manchester, circa 1900) who "married" my grandfather Henry Roberts in Montreal in 1928 before the pair came back to England in 1930. I say "married" as Henry was, at the time, married to someone else so they weren't actually married; legally speaking.
Henry died in 1945 after which Hilda continued to call herself Mrs Roberts so I suspect she never knew Henry was a bigamist. She left the home they'd share for 10 years, on the Wirral, sometime in 1946. I've no idea where she went although a relative of Hilda's, who sent me the photograph, remembers meeting her in Manchester during the mid-1940s.
Where she went, when she died, I have no idea but she had connections with Montreal, Birkenhead and Manchester.
The photograph is, I assume, a photographic copy of a print so its quite likely the "out of focus" impression it gives is as much to do with its copying as the original image. I think all point-and-shoot cameras before 1960 had a single 1:50 second shutter speed and, in those days, you didn't get the option of printing out individual shots; you had the film developed and printed in one go (contact prints or en-prints depending upon the size of the negatives). Whether 1:50 sec. would have blurred the cyclist is debatable.
I too have wondered about everyone but the cyclist being wrapped up. I've also wondered whether Hilda, who seems to be dressed up, was on her way to or from court in Birkenhead. The lodger she took on in 1945 was murdered although whether she was involved in the subsequent trial (Feb 1946) I don't know.
I think that the Manchester trams were gradually replaced by trolley-buses during the latter half of the 40's.
Whether any of this will help I don't know but I know you all like a good mystery!