Withdrawal from the American Union is governed by the Founding Charter of the United States which is also known as "The Declaration of Independence."
Also, the Brits are a nuclear power, and they can literally F*** up the European Union if the Union gets uppity about it.
Just goes to show, "speak softly and carry a big stick" is a pretty good rule for getting what you want.
For some reason people are perfectly willing to recognize your rights if you have the muscle to force them to do it if they become obstinate.
Actually the "Founding Charter of the United States" is Richard Henry Lee's Resolution, proposed on June 7th and passed by the 2nd Continental Congress on July 2nd.
The Declaration is really just the public relations announcement of what Lee's Resolution effected. John Adams thought that July 2nd would be our national holiday.
Resolved, That these United Colonies are, and of right ought to be, free and independent States, that they are absolved from all allegiance to the British Crown, and that all political connection between them and the State of Great Britain is, and ought to be, totally dissolved.
That it is expedient forthwith to take the most effectual measures for forming foreign Alliances.
That a plan of confederation be prepared and transmitted to the respective Colonies for their consideration and approbation.