The UK has some working holiday programs for young adults - but not with the U.S. (Would Canada suffice?) Otherwise, unless you have a valuable skill, a great deal of wealth, close family connections, or simply get lucky and win the so-called green card lottery, no, you cannot simply settle in the United States because you want to. (Even citizens of the British Commonwealth, like Canadians and Australians, can't simply move to the U.K., even though their countries were formerly tightly politically connected to the United Kingdom in relatively recent times - in Canada as recently as 1982.)
Go to the U.S.'s immigration website and see if you qualify - but based on what you've stated in your question, it's highly unlikely that you would.