Moving to the U.K. as a musician

I'm an American in music school at the moment. I've wanted to move to the U.K. for a very long time, and fully plan on doing so while I'm still young with no ties holding me down.

I plan on working in cruise ship showbands for a year, two, or maybe more after I graduate- I've auditioned once for Carnival...wasn't quite ready, but next summer I will be. Hopefully I can get my foot in the door during college, which will allow me to work on ships after graduation, and save up a sizeable nest egg while not paying rent, bills, or food costs.

When I feel I have enough savings to tide over a move to a new area, that's when I'll try to do it. I've been doing some research, and if seems that a visa for the U.K. is somewhat difficult to obtain; student visas are the easiest; won't be my category. The next is if you're being sponsored by and employer there and will have work right off the bat; also not me. So for a freelance gigging musician, what would be my best course of action? I need to one or another prove that I can contribute to their economy and society...difficult as a musician!

Anyone have experience in this, or know someone who has? It's my dream to live in and/or around London, and I really want to make it happen, so I can start preparing now!

Thanks!