Reporting of Stock Sale in a Foreign Exchange.
Generally speaking, when you sell the shares in a UK, you would have to pay U.K. capital gains tax, assuming you generate sufficient capital gains that would be subject to UK tax.
Assuming you exceed the exemption limits, you would be subject to UK Capital Gains Tax. This amount of capital gains tax that you pay to UK would enable you to claim a foreign tax credit on your U.S. Individual Tax Return that you can offset against your regular tax.
The capital gains in the UK would be subject to US capital gains tax of course. But, the taxes paid in the UK would offset the US tax liability to some extent.
I recommend that you should maintain a proper record of all the transactions that involve the cost basis and sales prices as well. You should also try and have the exchange rate applicable at time of purchase and sale to convert into US dollars as well. Thus, you can report the Stock Transaction in US dollars on your US Individual Tax Return.