Rod, with much reference to the 3rd Edition of British Planemakers, we'll have a go:
Alexander Mathieson & Son (Ltd), they were one of the the most prolific makers, Alexander starting the firm in 1822 (later claimed 1792 simply because they'd bought up John Manners who had indeed started then - cunning devils!) and continuing until the 60s when Record bought them up - although apparently plane making ceased during WW2. At various times they had works in Glasgow, Edinburgh (taking over J & W Stewart), Dundee (J Dryburgh) and Liverpool. There's also an Aberdeen mark listed.
That mark seems to be like one shown as being used between 1855 and 1870 by which time they were at the Saracen Tool Works, 11 (&13) East Campbell Street.
I believe it's the (hammered) grooving half of a tongue and groove pair, unless it's a drawer or drawer bottom plane for grooving the sides of drawers - but I frequently get in a pickle with wooden planes.
Next, Varvill & Son, 1829-1840, 17 Micklegate, York. Lot of Varvills, lot of planes made by them in various guises. Looks to be a tongue and groove pair (see disclaimer above!). The 3 is presumably a reference to the size - could it be 3/8"? Groyse (or Groves? Maybe it's just the pic) could still be an owner stamp despite the neatness. Not all of them hammered their ruddy names all over everything like the so-and-so who's tools I'm going through at the moment... #-o
Finally John Cox, and the profile has me stumped to be honest, but that doesn't mean anything. That very mark is shown and says likely to date from after 1914, so I'll skip the detail from 1883 until then:
Cox, John, Brimingham. 233 Bradford St 1908-1912> (i.e. beyond then is likely but no firm evidence found)
220 Bradford St 1921, then
Cox, Frank, 220 Bradford St 1921-1931. Sez:
John Cox was one of the later proprietors of Cox & Luckman. Although he was entered in the directories, he did not appear to have made many planes on his own account.
Under Cox & Luckman (1839-1914) sez John & Frank Cox probably continued to use the C&L mark after 1914, hence not many John Cox ones about I assume.
Cheers, Alf