Reputation/network of UK universities with US employers?

Something I hadn't thought about in terms of choosing a school is the reputation of the school outside the UK and how easy it would be to transition back into the US workforce (lots of if's here, but I want to make sure I'm not making life difficult for myself later). 

Not necessarily just how well-known or well-regarded the UK universities are (although that info is nice too), but also in general how well connected the universities are with US employers and whether they have networks of alumni in the US, etc.

I'm looking mostly at LSE (which I know is well known worldwide), Queen Mary, Royal Holloway and King's.

Thanks!!!

I can't speak to reputations/networks with employers, but I think many of the  older universities (Russell Group et al) will historically have quite a lot of American alumni and may well have alumni clubs in the US (The University of Sheffield definitely does, just to give you an example.)