Hi Bluegrass Lass,
Welcome to 'due diligence & research' !
You're not the first to have this idea, nor will you be the last. However, seeing as you are in your early stages of thinking, asking if it'll be successful is extremely vague. For instance, what sectors of retail goods are you considering making available to Americans living in the UK? will you be able to source locally the goods you are thinking about at a good enough 'wholesale/trade' price? how will you ship the goods over? will they be high value items? do you think the demand would big enough to supply? could you expand and also appeal to UK nationals as well ? ... and plenty more questions.
I do something along these lines, with goods that are available in the US that are not available here. Still early days for me as I have some projects and concepts going along at the same time, however in a nutshell, I'm focusing on a specific niche area of the market based on what consumers/end users are trending/looking/asking for and my area is Automotive/Automotive electronics. So I've specialised and I think it's something you'd need to do as well.
You'll need to be aware of shipping costs, taxes and import duties and if applicable, any warranty and return issues as well. On top of all that, you'll also need to be accepting of all the responsibilities of running a business - so start up costs, advertising, sourcing, accounting, stock storage, legal & accounting aspects on everything etc etc.
There's a whole lot more about this sort of thing, but it's way too much to type up here.
Good luck !
Cheers, DtM! West London & Slough UK!