Or you could go to any third world country (waves flags) and get your license with a lot less effort, last time I checked it was only a number of written tests, 40 hours of flight time, the 10 hour solo time and the examination.
As for price... you can get as low as 50$ thousands which is around the price of mid-high range SUV or twice the cost of a Mini Cooper Salt (at least where I live). The Piper PA-23 250, or the Cessna 402 both are around that price range if you know where to look and both should be able to cross the Atlantic if you look for the smallest possible water leg on the Northern Route (though the reason for such a low price probably would imply that it shouldn't be used for such a trip). Even then, you can probably split the payment of the plane on parts or split it along with other aviation enthusiasts willing to share the plane and maintenance costs, in which case you could look for something slightly better at a slightly higher price.
Alternatively steal the Spirit of St. Louis.