Hi Mat - Would agree with Tony that these may well not be as old as we're tempted to think, and my thoughts on origin would be Continental possibly, but very difficult to be sure of anything. I can't quite see from your pix, but am assuming there is no evidence whatsoever of a pontil mark, which just might suggest a more modern manufacture - if for example there is a lack of wear, and bearing in mind the non-lead aspect.
You don't mention extent of wear - or absence of.
The size and shape are similar to tumblers from the second half C18, of that there is no doubt - they were often almost as wide as they were tall and with pronounced tapering sides .......... later tumblers became taller and narrower (and made to higher quality), and with straighter sides.
I could be very wrong, but my problem with these is that the type of moulds used prior to the Victorian period (when factory pressing/mould making became commonplace with mass production) - were primarily to convey patterns/decoration to the outside of the glass, and these are plain.
Tumblers from Europe from the middle or second half C18, show mould decoration in the form of wrythen moulding, gadrooning and moulding in the form of flutes, and are blown usually, leaving a scar on the base.
If these were C18/early C19 I'd expect to see considerable wear (bearing in mind their utilitarian appearance)
and some remains of a pontil scar. I certainly think wear is a major factor here, if we want an early date.
Sorry this tells you really nothing positive about yours - and since you've been waiting for a few days have to assume all the tumbler experts are on holiday