Unlike most other jurisdictions worldwide, the US levies tax on its citizens irrespective of whether they live in the US.
This means that a UK resident US citizen is often exposed to both US and UK tax simultaneously.
The extent to which that individual’s wealth outside the UK is exposed to UK tax depends in part on whether that individual is either UK domiciled (that is, they consider the UK to be their ultimate, permanent home) or deemed domiciled (that is, they are not actually UK domiciled but, because of the individual’s circumstances, the UK will treat them as if they are UK domiciled).
This different approach results in UK resident US citizens often being exposed to tax in both jurisdictions at the same time.
If that individual wants to avoid that double taxation then, unless they are eligible to claim a foreign tax credit in one jurisdiction for tax paid in the other (which is permissible in certain circumstances), they may decide to leave the UK. However, exposure to UK tax does not stop as soon as the individual ceases to be UK resident.
What tax does a UK resident US citizen pay?
Income tax and capital gains tax
A UK resident US citizen ("P") is, by default, subject to UK tax on their worldwide income and gains, known as the 'arising basis' of taxation. However, if P is neither UK domiciled nor deemed domiciled, then they are eligible to be taxed on the 'remittance basis’ of taxation.
This means that P only suffers UK tax on UK income and gains, or on foreign income and gains that are 'remitted' to (that is, brought into or used in) the UK by, or for the benefit of, P or a 'relevant person' – a class that would include P’s spouse and minor children.
The remittance basis can be very efficient if an individual has significant foreign income and gains that they wish to shield from UK tax. However, since P is also a US citizen then those same funds will likely have also suffered US tax as they arose.
This means that P may be exposed to double taxation if they later bring those funds in the UK, that is, firstly to US tax when the funds initially arose, and then secondly to UK tax on the remittance of the funds.
P may be able to claim a foreign tax credit under the US/UK double tax treaty for the US tax already paid, however this is generally only available if the funds are remitted in the UK tax year in which the funds arise and, even then, usually only on certain categories of income and gains (such as those linked directly to US real estate and US dividends).
Given the above, P may be better off simply falling back on the default arising basis, since US and UK tax would both be levied as the funds arose and so the likelihood of obtaining a foreign tax credit is usually greater.