Chemist is one of those occupations that has several meanings, each of which brings another web of meanings and qualifications.
From what you say, my initial suggestion would be that she worked in a chemist's shop. (Chemist = Pharmacist ). Since my GGF Bruce did similar, I can confirm that in the 1920s it was just about possible to do that without formal qualifications. GGF also referred to himself as a Druggist. Even by that time, regulations were coming in that mandated that certain substances could only be dispensed by formally qualified Druggists. Which he wasn't as I've checked the Registers. Nevertheless, there was still plenty of stuff that he could dispense and my father, as a little boy, would stand there wide eyed as his GF made up stuff on the brass scales.
I believe that the registers in question were:
The Register of Pharmaceutical Chemists
The Register of Chemists and Druggists
The latter contains those with the minor qualifications - but I think that everyone in there had to have a formal qualification.
The Society of Genealogists library has just 2 copies of the latter for the interwar years - nothing like as common as Medical Directories.
The Internet Archive has The Register of Pharmaceutical Chemists and Chemists and Druggists for (1885) and 1919; Hathi Trust has 1885.