Paramo was set up in Sheffield at about that time, (WWII) by a known Sheffield manufacturer (Parramore and family, of Chapeltown, est 1924 near Sheff).
Their standard engineer-type bench vice is similar to, but not exactly the same as Record and Woden (separate companies, later joined) who from about 1900 both copied the ''Handy'' line of Parkinson of Shipley near Bradford - originally made from the 1880s. Parkinsons plastered (actually cast in) their name all over their quick release (Perfect) vices but for some reason usually only a sticker (almost always gone by now) for their Handy line (the second version of Handy often have Reg Des No 689821 cast in). Other Sheffield companies including Rededa, Wards, Marples also made or had made a range of such vices (usually not the big ones).
I have compared Record, Woden, Paramo and Parkinsons pre 1960 equivalents -- if anything the Paramo was the most solid and smoothest/least wiggly, followed by Parky, Woden and Record in that order (little in it), but it was not a controlled test - they may have had different usage and the 'smash with a sledge ' test was not done -- could have given a reverse result.
Back to your question -- I think Parky started the 00 to 8 numbering and most makers have a similar jaw width for the lower numbers (00, 0, 1, 2, 3) but then they might diverge, and some have A sizes (eg 1A) meaning smaller than 1 but others it means larger.
You need some old catalogues for the sizes (not too hard to find online) but they start with 00 - 2 1/4 ins width - useful table size, go up to about 7 ins big beast.
(I'm feeding Vono with more info for his book on English vices).
