regret to say that like most people who collect drinking glasses you are destined to always have a few which will remain of doubtful origin and/or date. Those who collect C20 signed studio glass don't know how lucky they are - but then they miss out on all the wonderful history.
Don't know which books you have, but I notice that in Hajdamach's 'British Glass 1800 - 1914 - under reproductions etc. - there is an example of a wineglass which might represent a typical source from which your rummers had originated. Admittedly the colour is amethyst (all the more desirable - they didn't go in for half measures, so it appeals to the greed in all of us
) but the shape is very close, and the caption says.........
"wineglass made by L. & S. Hingley, Wordsley, early C20, height 4.7/8" - rough pontil mark and capstan shape stem etc."
Obviously copying an early C19 glass, and doubtless would confuse most people, unless the lack of wear and excessively rare bowl shape rang alarm bells. If it looks too good to be true - it probably is.
Around 1900 Richardsons were offering very accurate copies of George III cut glass patterns - although I don't know if their efforts extended to drinking glasses.
Hill Ouston appear to have been copying just about everything from air twist spiral drawn stems and cordials of the 1740's to thumb cut ales of the 1860's.
All of which is a good reason to buy books and try to handle as much material as possible, and when buying remember all the golden rules, colour, foot/rim proportions, wear, stones/bubbles, weight etc.
Very unlikely you'll be able to attribute a maker to yours - might have been one of a number of sources - Continental perhaps - attached is another blue rummer - snapped pontil etc., some good signs of wear, shape typical of early C19 and rings like you wouldn't believe - but as to origin I've no idea, and a reproduction I suspect.? But the searching is always good fun.
I'd recommend both of the Hajdamach volumes if you don't already have them - plus Bickerton for C18/Regency drinking glasses.