if you're working on something completely location agnostic and you're getting a lot of valley investor interest around demo day, it probably makes more sense to stay in the US than return to the UK (that's what we did).
"Running a business" is specifically forbidden for visa waiver or B1/B2 visa visitors; besides, I suspect they won't be too happy if you repeatedly "visit" to the extent that >50% of your time is spent in the US. H1-B seems to be a lottery and infeasible if you own the company and are employed by it. I have no idea if we'd qualify for an EB-1, and E1/E2 seem more geared for owners/employees of bigger companies than recently-formed startups.
There seems to have been a string of originally European YC-funded companies that successfully moved to the US, yet there are examples where founders are "stranded" in Europe (e.g. Dailybooth). I vaguely remember an article written by one British founder of a YC startup some years back who got in via an E2, but I can't seem to find it. It would be extremely interesting to hear about past experiences with this; I realise it's possible that there's a good reason why everyone keeps quiet about it.
I just spammed Ian Hogarth from SongKick on Twitter, asking him to weigh in. I'm curious to hear his thoughts on it.
It's hard not being based in the Valley though and means a lot more travel if you want to close major distribution partnerships. You have to appear like you're based in the Valley to really compete for deals.