Yes ... it's 90 days, but the day of entry and day of exit don't count: you can fly in on Monday morning and out on Wednesday evening and that's only one day's residence for tax purposes (there are people who live in the Channel Islands or the Isle of Man who do this - I'd hate it myself). That's "non-resident and non-domiciled".
Or, if you have any legitimate connection with any foreign country (born there, family there, citizenship there, previous residence there, or whatever), you can elect to be permanently UK-resident but still not "domiciled for tax purposes" in the UK: under the new law, doing this is now limited to 12 years, and means that you still pay income tax on whatever you earn within the UK but you pay only a fixed £30k per annum in respect of all overseas income, regardless of how much it is. That's "resident but non-domiciled". And you can choose when the 12-year period commences. These are known as the "non-dom regulations", and a few thousand people - including some British citizens - take advantage of them.
If the actual "work of trading" that produces the income is done within the UK, then the UK's HMRC (formerly "Inland Revenue") will want to tax you on it, but they have to prove that, and of course there are people whose trading income is remitted from an overseas company (registered wherever they like, where they have a server from which the trades are made) as "passive income", who get away with not paying UK tax on it. You need to be earning quite a bit, to make this option viable, and it's (at least) "questionable", if the trading decisions are actually made within the UK. But there are people doing it successfully, and the British government doesn't necessarily want to lose them, because exactly as you say, they pay UK taxes on their spending etc anyway.
