If I am buying a big name product that is likely to have a counterfeit problem, the seller is usually going to be amazon direct or the manufacturer anyway as big products are stocked by Amazon directly, the stuff that isn't, is usually more generic or niche and not usually a type of product that matters since it's something fairly generic anyway, i.e a dish cloth, tape etc.

I am not sure if it's just less of an issue buying from Amazon UK or it's the type of stuff you are buying, but from what i've read it seems like it's mostly an Amazon US issue. Most things in the UK are not from third party sellers unless you are buying a generic item that is effectively dropped shipped from AliExpress like a fancy dress dinosaur costume.