If you are non-domiciled in the UK, what taxes would you pay on an offshore account if you brought it into UK?

I'm trying to understand the "remittance basis." You wouldn't pay tax on it as if it were income right? Presumably, such a person would doent that they have an offshore account as a non-dom in their tax forms, but just not have to pay UK tax on it as long as they don't bring an of that money into the UK. Am I right on that? But then, if that account just constitutes your net worth, and it doesn't grow that year, do you not pay any taxes on it that year if you bring it into the UK? Do you just pay taxes on any income the account generates in the future as a UK bank account?