I'm sure that Neil isn't contesting the derivation of the English word rummer as NOT having originated from the German roemer - and if you read his post again you will see that he has said only that ...... "the glasses pictured are generically known as rummers, as rum based drinks (punch, toddy, grog) were thought to have been the major purpose for their use." There's nothing wrong, historically, with what he has said, certainly as far as usage of this shaped glass goes in the U.K. - in fact a variety of spirit based drinks are known to have been drunk from what the British called a rummer.
Ivo and Peter are both correct, of course, regarding the fact that the British word rummer - to quote Tim Mills - "is an anglicized form or corruption of the Dutch word roemer." - a glass totally unlike those above, and which were used for blonde wines.
If you read Douglas Ash, G. Bernard Hughes and Geoffrey Wills - they all comment that rum was one of the drinks consumed from glasses of the shape shown above, and this was the extent of Neil's assertion.
Having looked again at Hogarth's 'Night' engraving, showing the inn sign of what is a British rummer shaped glass, my own opinion is that it's not possible to be certain whether this is a drinking rummer or toddy rummer - since within the area of the sign there is nothing with which to make a size comparison - one being a lot larger than the other. It's known that the toddy rummer (associated with the toddy lifter or ladle) was a commonplace item, and this drink was consumed from the smaller drinking rummer, so the depiction might be of either.
I'm also doubtful that we can say the contents of this particular glass on the inn sign are beer......... the slightly paler top section of the glass may simply be the more transparent part of the glass devoid of the booze - throthy heads (carbonated) on beer are probabaly more a product of the C20 than c. 1738.
Rummers with crazed bottoms (showing where the sugar crusher was used) are seen occasionally, showing that hot toddies were fairly common, although a variety of beverages were consumed from this shape of glass.
Pubs/inns with the name 'Rummer' were, apparently, not uncommon in London, Bristol and Liverpool.
Isn't it a shame Sue, that you can only dream of fondling them - but I agee that they are a type of glass of great social comment and come from that most interesting of centuries when the British, depending on your point of view, were blessed with Hanoverian monarchs.
And..............as to Robert's comments about penny licks - as you can probably imagine there appears not to be a book devoted these little pieces - very brief mention is made in Hajdamach's book, but don't think you'll find much else apart from that. If you do please let me know - presume you've seen my pix of some which I posted earlier this year I believe.
Regarding Neil's comments about not seeing the gadget mark............I doubt that you will........as Peter has now put us right on this matter, it has nothing to do with the Y or T shaped indentations on the underside of the foot (that is where the shears separate the pontil rod gob) - I've tried looking for gadget marks (which will be on the top of the foot anyway), and have so far failed to see any - but if you do find one and can photograph it, please post immediately.