Although many of the "period" Brit game guns will be marked 1 1/8 oz, which was the max load for which they were designed, you can be far kinder than that to them by shooting very light reloads. Low pressure, it doesn't make any difference if you're using standard American hulls, even if the chambers are 2 1/2". And while there are 2 1/2" factory shells available, most of them are field loads of an ounce or more (although RST and maybe another company or two do make some lighter short shells for targets and game). I've owned a number of Brit doubles, both 12 and 16, and have shot multiple hundreds of light reloads through them in a year, not to mention "full strength" loads of 1 1/16 or 1 1/8 oz during pheasant season. They'll have pretty much the same issues as any older gun, but you do need to remember . . . it's not the years, it's the miles (or the shells, and the amount of care/abuse the gun has seen).
Right now, the market for used Brit (and European) boxlocks seems to be somewhat depressed. Not a bad time to buy. And the recommendation of the Scott 700 series is an excellent one. They're newer guns with modern chamber lengths, etc, but handling characteristics like the prewar guns. Should be easy to find a 12, in nice shape, in your price range.
And the Webley & Scott 700's in current production are indeed coming out of Turkey. A friend just handed me a catalog he picked up at the SHOT Show.
