Quite remarkably, I've now been able to acquire an example of this exact design/pattern, and it would seem this very unlikely to be a tumbler. Mine has a lid (the moulding of which matches that on the body), which confirms my earlier thoughts that this was a two part item. The proximity of the moulding and profiled grooves are, in my opinion, definitely too close to the rim for this to be designed as a drinking glass. There are indeed three mould seams, and a flat ground/polished outer section to the base. In my opinion simply a rather inexpensive lidded storage jar - certainly not a pickle in view of the poorly fitting lid. The glass is quite clear and bright with some small bubbles - although doesn't appear to have any seeds/stones - and has a very dull clunk, so no lead content - and my example shows little wear.
Difficult to date really, might be late Victorian, or early C20 even, but there's no doubt that the pillar moulding is an example of an earlier decorative style (can be seen often on mid C19 tumblers) and is possibly confusing the issue - it certainly has the looks of being older perhaps than it is. Needless to say no marks on mine.
Unless I've missed it somewhere Neil, can't recall seeing if you'd commented on your whereabouts - this can, sometimes, help and/or provide some guide to the origins of a piece - and unsure if yours came from the U.K. or not. My example was from the South of England earlier today.