You are basically correct that you will not be double taxed. Basically you will be taxed in the country of your residential domicile which sounds like it is the UK. Assuming this is where you have your principle residence. You would be subject to UK taxation on the sale of the assets since you are a resident of UK at the end of the tax year.
The U.S. will impose taxation on the sale as well but you will most likely qualify for the "Foreign Tax Credit "(via Form 1116) and essentially get a credit for the UK taxes paid on gain. So essentially the US does not tax you on the gain. This is where the "double taxation" is eliminated.
So keep track on exactly what you pay to the UK on the gain on sale. The taxes paid to the UK will be used to compute the foreign tax credit to be applied from a US perspective.
Please let me know if you have any further questions on this or if something is not clear.