USAway,
You file for an extension, but it is not an extension of time to pay, just to file. You have to include an estimate of the total tax you think you'll owe with the extension.
Kate2112,
If you are a US citizen or greencard holder, you must formally give up your citizenship or greencard if you want to stop paying US tax; and even then, if you're rich, you'll still be subject to special US tax rules for another ten years.
If you are not a US citizen or a greencard holder, once you are no longer US resident you only have to file and/or pay US tax if you have US source income.
Yes, taxes paid in the UK are credited against US tax, but there are certain exceptions.