Written by James Cavanugh, Vincent Rose and Larry Stock, it dates back to 1924 and as far as I know is the only song with the word "thingamujig" in it. Rose & Stock also co-wrote the song Blueberry Hill, amongst many other credits.
Bud Flanagan & Chesney Allen were the most famous British stars in the early 20th century, comedians, singers, actors, they were stars of stage, screen and record.
The Umbrella Man was one of Flanagan & Allen's most successful recordings, the image of the Umbrella Man when sung by Bud & Ches conjures up an image of a poor East End London worker patching up poor peoples umbrellas so they can continue to wander the streets a little drier than normal, on their way to spend another night Underneath The Arches. Perhaps this view is far removed from the images conjured when sung by Louis Armstrong & Dizzy Gillespie. I'm cheered by a song that is about a man who repairs umbrellas, possibly a profession that no longer exists judging by the umbrella skeletons I've seen abandoned in the streets.
Here's a recording of Bud & Ches and below that Dizzy & Louis (I bet y'all wish you were on first name terms like me?)