A person who is resident in the UK and domiciled or deemed domiciled, is taxable on their world-wide income, on the arising basis. This may entail the submission of a Self Assessment Tax Return. A person who is resident, but not domiciled in the UK, is also taxed on their world-wide income on the arising basis, or they can elect not to remit a foreign income to the UK, that arises while they are resident in the UK.
If they choose not to bring the income to the UK, then it is not taxable in the UK in that tax year. If they choose to remit the income to the UK in a later year, then it would be taxable in that later tax year. If the income was generated in a tax year when they were not UK resident, this would not be taxable when brought to the UK.
To claim the remittance basis is criteria for completing a Self Assessment Tax Return. The residence supplementary page is SA109, is where you declare the use of the remittance basis and the amount of income not remitted to the UK. Tax returns can also be submitted online, however, to submit a tax return that included a residence section, required the purchase of 3rd party software.
A list of suppliers can be found at:
Self Assessment commercial software suppliers