I've just had hazy recollections of the "My Mums" cheapo brand of products 
that graced corner shops and the like during the 1980's... can anyone else 
remember it?

They did your usual  stuff such as cornflakes, bog roll, etc. But they also 
did cans of pop, which I always remember being quite nice, especially the 
cherryade. Except the cans, at the time were made of steel, so after a 
while they started to go rusty.

Now, how widespread was this "brand"? Can anyone remember when it appeared, 
and when it disappeared?

I think it got superceded with Happy Shopper, or Best Buy....

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http://www.mercuryvapour.co.uk <-- Main site. 
http://www.scribcam.co.uk <----- Webcam. Eww.