sweetpeach, your statement about 'not paying tax on income you keep outside the UK after you have been here for a while' is not really clear to me, but you seem to be saying that a UK citizen who is domiciled elsewhere and earning income there is required to pay UK taxes there, which contradicts what others have said here.
No, you are not required to pay UK taxes.
However, if you live in the UK and are not domiciled in the UK and you choose to pay tax only on the income you bring into the UK, you may have to pay a hefty penalty depending on how long you have lived in the UK.
So it is your choice.
If you have lived in the UK 7 out of 9 years,
either:
1. Pay UK tax on all your income.
2. Pay tax only on the income you bring into the UK, plus pay a £30,000 charge.
It's possible that for someone who has A LOT of money outside the UK, paying the £30k charge is the better way to go.
I believe you also lose your UK personal allowance (the amount of money that you are allowed to earn before you start paying tax) if you earn money outside the UK and choose not to pay UK tax on it. I think this happens no matter how long you have lived in the UK, but I'm not 100% sure.
I also believed that you are exempt from all these penalties if the amount you earned in the UK is only a small amount. Possibly £2000 or under?
Unless this has changed very recently and I don't know about it.
Maybe Guya can set us straight about this?
ETA: This applies only to people living in the UK, so the income from abroad would have to be things like interest from bank accounts, stock dividends, etc. You wouldn't be earning money (as in earning a salary) outside the UK because you would be living in the UK so you couldn't have a job outside the UK.