I never knew of the Onion Fair, possibly as it was held in Aston - unknown territory I'm afraid. I did know of Pat Collins famous fair - I recall, after WW2 it arriving in Shirley, Solihull usually during the long school holiday periods. I had noted the Ingleby Street, Ladywood address on the truck cab doors ( I was just as interested in the vehicles and fairground machinery as much as the rides). I went to Ingleby Street on one occasion to see what sort of place it was. It was just a dwelling house, a back to back style most likely, in a long terrace. I don't know whether Pat actually lived there: to me, at the time it seemed unlikely.
Is the fair still in operation? I guess Ingleby Street has long gone.
The Onion sellers, with their bicycles, are less frequent these days. They tend to be found with the French Food fairs which visit SW England each year. The Plymouth - Roscoff Ferry is their usual route to the UK.