Oooh! That's a good one!
Definitely not in either Sketchley's or Gales & Martin.
Your best bet is to get in touch with the Cutler's Company:
https://cutlers-hallamshire.org.uk/contact-us/
My guess, informed by the apprentice registry, the blade design, and it's non-inclusion in the most likely directories is that it was made by one of the Thomas Robinsons. There were three in the timeframe of 1750ish to 1765ish, which is when I'd guess that razor was made.
There's a whole mound of Robinsons in the apprentice registry, but those are the only ones in the right time and trade.