Stephen,
There were several tyre options for the 350EW, but the easiest way to identify them is the spokes are laced into the brake drum, and the hubs where made from heavy sheet metal and tubing.
Hubs. The 600EW used one-piece hubs turned from (presumably) a stamping and a conical spline for detachable brake drum. These one-piece hubs were also used on the 1926 OC. I think the first lightweight to use the stronger hub was the B29, as it advertised detachable brake drums. The A29 likely continued with the cheaper hub, but by the time of the A31, all the lightweight models had the stronger hub and detachable brake drums. As did the all heavyweight models from 1928 on. That hub was used on nearly all models through 1938 (excluding Works racers, the Bantam, and the Quickly-Detachable rear hub option of 1934-35).
Rims. Well-based rims (wired-on tyres) first turn up on the S5/S6/T6 models from late 1929 onward. Lightweight models continued to use the old style rims for quite a long time (1934-35?), excluding the lightweight colonial/touring models of 1930-32. For example the H3 (of 1930) had wired-on tyres and the L3 did not.
540mm for a well base makes it a 21 inch rim I believe? I do not know if you are measuring the outer diameter or the bead diameter, but it seem too large to be a 19 inch rim, which is what Douglas used for well based. Were it a 19 inch rim (483mm at the bead), then the first picture could be a wheel suitable for a S5/S6/T6 or any heavyweight model to 1938, or one of the 'colonial' lightweight models from 1930-32. Otherwise I assume the wheel has been re-rimmed.
The second picture of the beaded edge rim could be suitable for the OC, 600EW through 1929, or the G/H of 1928-29. The tyre options for the 600EW were 26x3, 700x80mm, and 710x85mm. While tyre sizes are not mentioned for the other models (except for the G/H28, which were 710x85), presumably the same options were available to them as for the 600EW.
-Doug
