If you scan over the chapter headings on the Vauxpedia website you can see how the model designations were broadly alphabetical from when GM took over the company in 1926, although oddly beginning with the S type, followed by the R and T and then the VX and VY Cadet.
The sequence then began again in 1933 with the ASY and ASX, BY, BX, BXL, then DX, DY and GY, GL etc. The missing letters in that sequence were later used for the C series vans, E series Cresta, Wyvern & Velox and F type Victor. Which brings us back to the H Type in 1937 followed by the I and the J.
After the war the HIY, HIX, I and J were replaced by the one size fits all L-type. The H type small car was then re-introduced fifteen years later in 1963 - beginning again with the HA.
It all sort of makes sense - if you close one eye, tilt your head and stand back a bit!

And I'm still not sure what happened to the K type...