I'm quoting from Fowler's Modern English Usage.
In AmE, 'one' is followed either by another 'one' (or one's) or by a third-person pronoun 'he' or 'she' (or, to avoid gender problems, occasionally 'they'), or by 'his' or 'her' or 'their', whereas in BrE, another 'one' (or one's) follows: (AmE) I...