You are partly right...
I offer this from a shotgun shooting Brit...
"With English proof the barrel wall thickness tells you how much metal there is left in the barrel tube walls but that measurement on its own is only a very small part of the barrels state of health. To us Brits it is the bore diameter measured 9 inches from the breach face that can tell you a lot more about what has been taken away and what is left as far as the guns proof life expectancy is concerned.
You did say 2 ½ inch chamber so I assume it is a 12 bore and the starting figure for a 12 bore barrel is .729 inch measured at 9 inches from the breach if the gun started life at the correct size give or take a few thousands of an inch. The other and most important measurement is .740 inch at 9 inches from the breach because this is the last acceptable size a 12 bore gun barrel can be before it goes out of this proof range but the working end size is usually .739 in reality to have some working life in the barrel.
So between .729 and .740 you can see at a glance if the barrels have been fine bored to remove some dents or pitting etc. and more importantly how much wear and polishing can be done to the bore before it reaches that stomach churning figure of .740 which here in the UK means an oversize re proof with the chance that the gun can end up as a pile of high value scrap on the proof house floor.
I hope this is of some help to you."
Back to this gun, a true measure of bore diameter at 9" would go a long way to telling the 'health' of the barrels.
I do note that there are three London proof marks (the ones with the crowns or sword) visible on the right flat (the same appear to be on the left flat as well), one of these groupings is for 'Nitro Proof' (the sword). Further, there is another proof (LC/12 mark) from London/Birmingham.
This suggests that the gun may have been re-proofed at some point in the past.
I list a link to a good source for UK proof marks at the top of this page.
I'd like to see where the top lever sits with the gun fully assembled - photographed from above, as well as the serial number on the gun itself.
The owner states that the metal has been refinished - a respectable job (the case coloring could be nicer...). Looks like the wood has been worked on as well (it sits very flush to the action, which is a bit unusual - it would have been 'high' on a new gun), but again, a re-finish of the wood is fine, just so long as it is known (from the looks of it this was done a while ago).
I would state that this is a GOOD price for the gun as offered. If I were to buy it I would want to see the top lever position, be sure the action is 'on face,' check bore diameters, and evaluate the metal re-finish in person. A good look down the bores for pits or dents and a once over on the wood.
That being said, I restate my above comment: for the money, as offered, this could be a really nice deal...