US citizen, non-domiciled resident in UK - which country's tax laws apply?

As a US citizen, you pay taxes on worldwide income. If you have $10K or more in off-shore accounts, you have until 6/30 of each year to file a TDF 90-22.1 form with the treasury. (Failure to file the form can lead to VERY steep penalties.) If those accounts pay interest, yes, it's fully taxable.