https://www.thefashionlaw.com/resource-center/gray-market-go...
Honest question, I really don’t know
One side question: how do you manage the warranty? Presumably as the reseller you will need to handle the legal minimum warranty (how long is that in the US?) by shipping the article yourself back to the UK?
With the exception of specific types of products (cars) or situations where consumers are gravely at risk (recalls), there is no mandatory warranty in the US. Your only requirement as a reseller is to pass on any warranty from the manufacturer, and allow customers to read a written warranty before making a purchase.
It’s one of the reasons why Amazon takes such pains to make the questionable assertion that they are at arms length for every transaction. Fraudulent or grey market stuff often fails the fitness test.
The same crap used to happen with fake cameras and electronics in Manhattan. The stores would “go out of business” and reopen the next day under a new guise to avoid legal consequences. Now you just create a new merchant on Amazon.
https://en.wikipedia.org/wiki/First-sale_doctrine