Hi Meg,
Your best course of action if you want information about getting a work permit is to contact your nearest British consulate AS SOON AS POSSIBLE to ask about your options, because you need to get work clearance before you arrive in the UK.

Saying that, the solution is actually to find a company that will hire you while you are in America, do the admin job for getting your Visa and welcome you in the office in the UK. American companies in London or even any company that deals with america will be more likely to do that of course.

Anyway, it's like any job. If you suit the position, hiring you from abroad shouldn't be a big problem...

Good luck

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