Yes. You do have to pay taxes in the UK as well but it depends on how much you have already been taxed in the US.
Say, you have to pay 20% tax in the UK for your earnings here. You ARE required to pay the same percentage on your foreign income as well. Now, if your "home" country already taxed you at 10% (for the sake of example), then you only need to pay the "remaining" 10% in the UK.
However, the tax law in the UK does allow you to choose between "arising" basis and "remittance" basis on your income from the country you are domiciled in. What I have explained above is based on when income "arises." But the laws are complicated, and you are almost always better off by paying it on "arising" basis.