You may still find imperial grub screws at the more 'old-fashioned'
ironmongers (ie: not B&Q) or more established machine equipment suppliers
(ie: not Machine Mart). I have a few in stock in my workshop, and I bet if
you know anyone in the toolmaking trade they'll be able to help you. But it
will probably be easier to cut a bit off a set screw or bolt, and saw a slot
with a junior or standard hacksaw. Beware that it will be 'softer' than the
proper thing though.
I could be mistaken, but I'd have expected 1/8" x 40 (1/8 BSW) would be
too fine for that purpose. Could it be 4BA, perhaps?
Take the door knob to your nearest engineering suppliers and get them to
try different screws until they find one that fits. Then buy at least
two per handle and a small quantity of matching nuts -- you'll need the
nuts to restore the screw thread when you cut the machine screw(s) to
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