Clarkes sold shoes (well, children's shoes anyway) in different widths (expressed by a letter) as well as lengths (expressed by the usual number) but I'm not sure if they still do. So, that machine might have actually worked. When I buy shoes, it isn't just the size (length) that matters but the width and shape of the shoe. I find that even if there is plenty of toe room, they can often be tight at the sides.
It isn't uncommon to have one foot bigger than the other, but they don't allow you to buy odd sizes. You would need to buy both sets.Measuring never helped me much and still doesn't; I have always had a full size difference between my feet.