I've seen it quoted online--Longstone in England IIRC, but can't find it today--but my back-of-the-envelope calculation it's a bit over 25" total diameter. This is arrived by:
15" wheel diameter = 381mm
165mm tread width x .8 = 132mm ('normal' profile--i.e. non 'low-profile'--radial is generally considered to be approx. 0.80 aspect ratio. That is, tire is 80% as tall as wide)
132mm X 2 = 264mm
381mm + 264mm = 645mm
645 / 25.4 (mm/inch) = 25.39"
Later cars came with a radial option, I believe, though I can't recall the name and don't have my BMIHT cert. handy ('Road-'something) and, if I'm not mistaken it was 165mm tread width. Some owners--maybe they're on this forum--prefer 185R15, which gives a total nominal (unloaded) height of 26.65", which may be closer still to original height (the original radials may have an aspect ratio greater than 0.80).
If I had to pick a number, I'd guesstimate original, nominal height was between 25.5 and 26 inches.
Our speedometers are calibrated by 1,000 turns of the cable equals some distance (1,520' comes to mind, but I don't know from where), so if you know that number you can calc how far the tire would travel--hence its circumference--and from there get its diameter (though that might be the loaded--'squashed'--diameter).
Good info here:
https://www.longstonetyres.co.uk/page/vintage-tyres