I asked a few years ago but my search skills in this site are poor and I can’t find the post.

I think it might be worth another try as ‘AI’ has been invented since then and I had a conversation with it to see what it thought:

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Title Idea:
Need help identifying this antique English shop-made tool/jig stamped “W. H. MEARS”

Physical Description:
Base: A 3-inch high, dark English oak block with mounting screw holes at both ends (designed to be permanently fixed to a bench or surface).
Metal Bed: A flat, smooth length of steel roughly 11 inches long and 1 inch wide, screwed onto the top of the oak base. The sides of the steel plate are entirely hand-filed, leaving a visible manual finish.
The Clamp: Located at one end of the steel plate. It is a 1.5-inch long piece of steel, slightly bevelled on the underside to make sharp contact only at its front and back edges. It is tightened via a central thumbscrew.
Capacity & Clearances: Because the tightening screw goes straight through the middle of the clamp, material cannot pass under it. It can only hold the literal dead end of a piece of material (clamping depth is limited to about 1cm). The vertical capacity is under 1/16th of an inch.
Wear Marks & Residue: There is a distinct horizontal scratch running lengthwise halfway down the right-hand edge of the steel plate, which might be a sign of  wear from repetitive tool use. There was also brittle, flaky, amber-colored residue (likely old animal hide glue or shellac) trapped in the hairline gap between the steel plate and the oak block.
Maker’s Mark: The name “W. H. MEARS” is punched in a single strike with a common outline border onto the wooden oak base.

Best Guesses So Far:
Because the edges are entirely hand-filed and the name stamp features a custom journeyman’s border, this is a bespoke, one-of-a-kind craftsman-made fixture rather than a mass-produced commercial tool. Based on the 1cm dead-end clamp, the 12-inch length the top theories are:
A Marquetry / Inlay Stringing Trimming Jig: Used by a 19th-century English cabinetmaker or musical instrument maker to prepare decorative inlay borders. A 1/16″ thick strip of wood stringing would have its 1cm tip anchored in the clamp, allowing the artisan to pull it taut down the bed. A specialized edge-scraper or “scratch stock” with a guide fence would be drawn down the right edge (causing the horizontal scratch) to shave the inlay to a perfect width. The flaky residue would be hide glue/shellac used to stabilize the brittle wood.
A Precision Filing or Component Dressing Block: Used by a clockmaker, watchmaker, or gunsmith to dress or polish ultra-thin, flat steel components (such as clock click springs or regulator scales). The 1cm tail of the flat stock was clamped, and an abrasive stone or file with a edge-guide created the track on the right side.
A Hand-Drawn Wire/Pin Straightening Block: A tool used to pull and flatten fine coiled metal wire or pin stock against a smooth surface, though the absolute flatness of the steel bed (no grooves) makes the flat inlay theory slightly more likely.

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My guess is that you put sandpaper under the clamp and then use it for sanding/polishing somthing held between 2 hands. Maybe sharpening or stropping.

I can’t remember if I got it in a second hand tool shop, or an auction of a clock makers workshop.