I moved to London from the States and don't regret it for a second! I've fallen completely in love with it. There is an abundance of any style of music you want to play and amazing stuff happening every night at surprisingly cheap prices. For example, if you're a musician you can get into Ronnie Scott's for FREE every night of the week after the main show is over. There are fantastic local acts doing the late set every night. There are some great jam sessions; jazz, blues, hip-hop, bluegrass, anything, really. There are some roda de samba hangs that are free. You can see the London Symphony Orchestra for £10. The list goes on and on.
There are, however, killer musicians all over town. You really need to have your stuff together. That said, London (or any big city) is a great place to GET your stuff together.
It took a little bit to work my way into the scene, but I'm making a living. It does seem as though there are more places to play (that pay at least), and more funding for the arts in London, and Europe, than there is in the States.
If you're dreaming of playing music as a living with great players every night of the week, I would highly recommend the move to any big city. Come to London! The first beer is on me.