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Working for own UK company whilst living in UAE

Yes, that's what I would do. UK is quite good as you don't need to register anything sorry you leave UK. You may want to get a residency somewhere, best in a country that does not tax foreign income such as Hong Kong. Even the US would be an option as long as you don't pass the substantial presence test you won't have to report anything. It is important to have an address somewhere. You must invoice your company in the end. But most important is to stay out of UK.