Wyoming is probably the only state left in the US that can still be used for incorporating that won't sell your information and will actually respect privacy laws... However, that may soon change too.
Nevada used to be #1 on the list, but they sold out a while ago and they do "share" director information with data corps. So, if privacy is a big deal to you, and you're strapped for cash, stick with Wyoming.
Sure you can probably go through all sorts of buffers and make it all complex and confusing... but that's a lot of hassle, and ultimately, not that tough to uncover/trace. Everyone and everything has a price, and your secrets and information... are not priceless. I promise.
Its really about what your intentions are.
If your intentions are illegal, according to US or UK law, then you're going to want to rethink that strategy and really ask yourself if its worth pursuing.
If its to make gobs of money and avoid paying taxes, and you're a US citizen... Again, you should rethink this goal and ask yourself if its really worth going to prison over or never coming back to the US either.... because if you think you'll get away with it, chances are you won't.
However, if your intentions are.. questionable, but legal in terms of you're okay with paying taxes to the US gov or any gov, and you're not practicing something on the big uber illegal list of activities (ie. drugs, money laundering without a bank license, human trafficking, etc..) AND you have the means to invest some cash too, then your options for privacy and security are wide open, but only to a point. It helps immensely, if you have amazing relations with political/government people directly. They can always assist you in speeding things up or not having to jump through hoops, but if you get into major trouble, and you think they'll bail you out, then you're dreaming...
Moral of the story...don't be a schmuck and don't do anything illegal. Way too much cash to make by staying legal. Blackhat/grayhat however, well, that's a different story.