Ok, this is all speculation until someone can come up with a catalogue picture or matching example in better nick, but I suggest:
It had an American style round front knob, not a panel plane square one - evidence is that this picture
shows a round, thick area in the casting, around the surviving stub. (DM - can you take some closer pics or comment on this?)
Also, I reckon the rear handle is original. It does not look like any saw handle; the shape is odd enough to belong to that time before one design dominated. For evidence, could we see how it is fixed to the casting please? Is there a screw up through the bed, or anything that might be screwed down into a lump or onto a stud?
This early US plane from the site Jimi linked to looks as if it might have a similar method to fix the handle:
Again, a closer view would help - as would more knowledge!
And Matthew - when you say Mathieson, can you point to a specific,
cast, model? I've only got scans of an 1899 catalogue, but there is nothing similar in there that I can find.