The truth is that you can’t!
Domicile is a legal concept and there are principles to determine it, but in general terms a person’s country of domicile is the country they consider to be their permanent ‘home’. They may choose to live elsewhere in the world but will usually retain strong associations with their country of domicile, including those of heritage, language, culture and family ties.
Domicile is really only relevant for the purposes of UK Income Tax and Capital Gains tax if someone has income or gains arising in jurisdictions outside the UK. This is where the option of a claim is in point. Such an individual may notify HM Revenue and Customs that they consider they are not domiciled in the UK and alongside that, they may also claim to be taxed on the “Remittance Basis”. This means that they are not obliged to report any overseas income or gains to the UK tax authority, unless they bring the funds into the UK.
The downside of making that claim is, for the first seven years of residence in the UK, limited to losing any entitlement to the tax-free Personal Allowance and some other reliefs. Once someone has been resident in the UK for at least 7 of the preceding 9 tax years, to continue to use the remittance basis they are obliged to pay an annual charge of £30,000. That charge increases to £60,000 per year for someone who has been UK-resident for 12 of the preceding 14 tax years. Obviously, if someone has substantial income outside the UK the remittance basis charge may be significantly less than the UK tax that would otherwise be due, but the advantage is time-limited.
Since 2017/18, anyone who has been resident in the UK for 15 of the previous 20 tax years is “deemed domiciled” in the UK and must report and if necessary pay UK tax on all their income, wherever in the world it arises.
The term “Non-Dom” is media shorthand for someone who may be enjoying all the benefits of a UK lifestyle while contributing little directly to the Treasury. The reality, of course, is that successive UK governments have not wanted to (overly) discourage wealthy individuals with strong overseas connections from living, albeit temporarily, in the UK and spending considerable amounts of their money here.