Life is probably a bit more complicated.
If you are non-UK domiciled and you claim this and the remittance basis on your UK tax return then what you bring to the UK (providing it is income or gains) is deemed to be net of the US tax.
So if you bring in income of - say - $80, and the US tax rate is - say - $20; then you are deemed to bring in $100 on which you owe UK of $40 less credit for the US tax of $20.
Sadly, these rules on remittances are horridly complicated.
Life is relatively simple if you remit just interest income but if you remit other stuff such as capital gains on US stocks or (even worse from a UK perspective) US mutual funds then the calculations are really really horrid (gains on sales of US mutual funds never qualify for the UK capital gains exemption that meggles mentions, unless the fund you've sold is approved by HMRC which is jolly unusual).
UK tax rates are a maximum of 32.5% on dividends - even potentially non-UK dividends -but up to 40% on things taxable in the UK but if wrapped in an ISA then can be zero in the UK but up to 35% in the US.
