When buying stockings, take into consideration the following:
Vintage stocking sizes are based on shoe size and not leg length or body weight. That is the end of the science the rest of the topic is an art where everything else depends on the wearer in terms of likes and dislikes and the original maker in terms of design.
Modern stockings stretch making shape and length less important. In general, vintage stockings do not stretch, although mesh stockings give more than plain knit.
Vintage stockings also tend to be shorter than modern equivalents (the dresses were longer). Some hosiery manufacturers (usually USA) did make short (S) medium (M) and long (L) whereas others marked the length on the packet or welt.
Different manufacturers tended to use slightly different proportionate sizing so you may find that your correct size in a particular variety may differ a little from one to another. This is the art and the only way to find your correct size is by trial and error.
I generally suggest a half size either way, but no more, should fit equally well. The UK/US size is a measure of the foot, in inches, from the tip of the toe to the rear of the heel. Length is measured from the top of the welt to the bottom of the heel.
My favourite maker of stockings and all sorts of wonderful faux-vintage lingerie is What Katie Did. You can visit her website here: www.WhatKatieDid.com and Email Me to request my size and preferred styles.
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