Capital Gains and foreign tax credits

As a USC and long term UK resident -   If I sell a stock in a US brokerage account and make a capital gain who do I pay the tax on this gain to so I can then  claim a foreign tax credit to the other.  So guess the question is who is first in line to tax this gain? 

I believe that the UK is the primary taxing authority here, so you would pay taxes in both countries, claiming a foreign tax credit on your US tax return. When completing the US return you would use form 1116 to claim the credit, marking the box “Certain income re-sourced by treaty”.

As a USC and long term UK resident -   If I sell a stock in a US brokerage account and make a capital gain who do I pay the tax on this gain to so I can then  claim a foreign tax credit to the other.  So guess the question is who is first in line to tax this gain? 

The UK has the primary taxing right.  Because of UK share pooling,  exchange rate fluctuations and the UKs CGT exemption there is often no element of double taxation.