Check chrisdew's answer above. It just doesn't work like that in the UK, or most places in the EU. If it was a totally different company, doing a totally different type of business, then you could argue the case that it was nothing to do with it. You would still have to pay income tax on any money you remitted into the UK though from your US or other earnings abroad.

In much the same way as the US treasury want's a piece of US citizens worldwide earnings, I believe.

You really do not want to mess with HMRC in the UK. They will chew you up and spit you out without a care in the world if you don't play by the rules.