Hi,
There's no one set way on how a US citizen should invest in the UK, there's far too many variables and preferences, products and services available !
Do take a look at moneysavingexpert.com and thefool.co.uk and from there, you'll probably be linked into various other online resources which you find is favourable to you and what/how you wish to invest.
Everyone is different according to their own individual financial circumstances which will affect on how and where to invest and in what type of direction. I'd love to 'invest' in another property to rent out, but it's just far far too expensive around here and in most of the rest of the country, so I've taken a different route.
Do also look into any legal and tax issues that may arise from your individual circumstances and I'd say it's well worth speaking to a tax lawyer familiar with both countries in order to cover yourself correctly as to what you'll owe etc.
Cheers, DtM! West London & Slough UK!