Yeah, I think you have it upside down and backwards.
Double Shotguns, specifically British 12 bore side by side guns are trading at "amazing" prices. What would have been $5000+ 10-15 years ago is now $3200.
Alternatively, if its a really light weight 28 bore or 410 with long barrels, plain border engraving, good chokes, and a long stock, that gun might have sold as a plain-jane gun 15 years ago for $4000 on a really good day, yet that gun would fetch $12,000 today.
I think you're conflating "doubles" as in shotguns with "double rifles".
Double rifles are about the same price in the UK as they've been for the past ten years. When brought over to the USA, properly regulated, gone through, and with the presentation of a test target showing ideal regulation, they are worth quite a bit more than a speculative rifle of unknown performance thrown up on a British auction site.
People don't know what they don't know so most of them get F'd on these types of purchases. You're going to pay $500-$1000 to get guidance, evaluation, inspection of the weapon during the 3 day return period (you always negotiate one) and a prescription for what work must be done on the gun. That work might take several craftsman and may take you over a year to complete. Most people just go do all this on their own because they do not know their own ignorance sort of the same way as most men answer surveys believing they could safely crash land a small aircraft and walk away. (Neither are correct, they underestimate the complexity and overestimate their proficiency)