Hi
As you are in receipt of foreign income, you will need to declare it in a self assessment tax return, in the foreign section,
If you are required to pay tax on the dividends in the USA. The UK/USA tax treaty allows you to claim a foreign tax credit of up to 15% of the foreign tax paid.
Please have a look at article 10 regarding dividends at
Uk/USA Double Taxation Agreement - 2002
If you are not already registered for self assessment, you can do this at
Check how to register for Self Assessment.
Thank you