The old British paper sizes were a bit inconsistent. And never matched the film sizes very well, which made enlargement a compromise.
but no one cared in the least.
Square negative were never exhibited square, it was not liked as a print format, nor was paper made for it.
All the larger sizes were used for exhibitions Often printed one size and mounted on the next size up. even though the proportions differed.
Most amateurs exhibited at 15x12 0r 20x16
whole plates and half plates were often used for postal clubs.
2 1/4x 3 1/4
1/4 plate 3 1/4 x 4 1/4
Post card 3 1/2 x 5 1/2 (Varied)
1/2 plate 6 1/2 x 4 3/4
Whole plate 8 1/2 x 6 1/2
10x8
12x10
15x12 (16x12 is a new size)
20x16
30x40
in the 50's Most of these sizes were stocked in Photo shops in packs of 10, 25,100 in three or four grades and in Glossy, mat, white fine luster, silk and in Cream and white in both Bromide and chlorobromide.... the permutations were endless. Some shops would stock these in Kodak, Ilford and Agfa, all of which also offered speciality papers as well.
Agfa offered a real silk velvet surface, that produced the most sublime blacks, but was fragile in the extreme.
All continental sizes were avilable to order. As were other tinted bases, and surface finishes.
How times change
The most popular white fine luster, is highly resistant to scanning, as the surface reflects as a fine overall pattern of light reflections.