The non-domicile rule is a distant echo of empire. It allows some residents of the UK to cite some other country as their real domicile and then, unlike all other residents, to pay UK tax on their earnings in the rest of the world only if they "remit" the money to the UK.
The idea of taxing anybody on this "remittance basis" was introduced when income tax was first imposed - in 1799 - in order to allow those who owned land in his majesty's dominions to escape tax on their colonial wealth unless they brought it back to England.
This remittance rule was then attached, for the first time, to the idea of a "non-domiciled resident" in 1914 to allow those who had been born in the colonies to live in England without paying tax on their foreign rents and stocks so long as the money remained abroad.
Today, however, the rule has been taken over by some of the wealthiest people in the country who can claim to be linked to some other domicile and who thus are allowed to escape UK tax on all of their income and capital gains in all of the rest of the world, providing they do not bring the money into the country.
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Apart from the Irish Republic, which inherited the rule, we can find no other country in the world which allows any of its residents to claim that their real home is elsewhere. The United States says it does not matter where you were born, if you qualify as a resident of the US, you must pay US tax on all your income and capital gains all over the world.
The Australians, the French and the Danes do the same if you spend more than six months of a year there. The Canadians and the Spanish do it if you spend 183 days of a year there. The Germans and Belgians and Greeks do it if your "customary place of abode" is there. The Japanese have a version of the UK domicile rule but only if you stay there for fewer than five years.