In London the Pellatt's produced glass for most, if not all of the first half of the C19, and made a very diverfe range of articles which did include tumblers, although they're probably best remembered for Apsley's patented sulphide plaques.
I'm not sure what to think of this NT 'tumbler' - the wheel engraving is of fine quality but not easy to date - my opinion is that it would pre-date 1846 - I'm sure it's a blown piece and not pressed. But the more curious aspect is its shape which is not that of a standard tumbler, and with that curve where the side meets the base it reminds me strongly of the top part of a carafe and tumbler/tumbler and up/guest water set.
The few sets of these things I had have long since gone but the short squat dimensions of this one may well be similar to the size of carafe tumblers.
I don't know what sort of start date carafe and tumbler sets had, certainly they were around in the middle of the C19, but how much earlier than that they might have started perhaps someone else might know.
Don't think you could ever rustle up enough evidence remotely to make the connection between Pellatt and Fox Talbot for this piece, but romantic idea perhaps.
