Like most countries, if you are resident in the UK, you will be subject to the UK on your worldwide income.
However, if you are resident in the UK but you are not domiciled in the UK, you can claim the ‘remittance’ basis of taxation. This means the UK will tax you only on money you bring into the UK. The remittance basis is essentially free for a certain number of years, then you have to start paying for the privilege, like GBP 30,000 per year or GBP 70,000 per year or something like that
So if you are am American and you are resident in the UK but not domiciled there because you are there temporarily then on the portion of your income paid from the US side of your firm to you US checking account you are not paying UK tax.
So you can be a Russian billionaire, buy a huge home in London, live in London and not pay any UK tax on all your assets which are in Switzerland or the Channel Islands or Russia or wherever.
Many people think that this is part of the reason that London property prices are so high and a lot of people are resentful that foreigners come in and drive up property prices. So the Labour party is saying it wants to do away with the non-dom regime so that if you are resident in the UK, then regardless of your domicile status you must pay UK tax on your worldwide income. But, basically, with the non-dom regime, the UK is one of the world’s greatest tax havens.
If labour wins then potentially this should be negative for London real estate pries and the pound as well.