But I still don't understand the issue.
The single person's allowance is £14,500 and the lower rate band is for the first £6,500 above that. So you can earn up to £14,500 tax free, earn £21,000 and pay 10% on £6,500. Earn over £21,000 and you then pay tax at 22% on the amount earned over £21,000, whether that is in one job or two.
As I understand it you can ask the Tax Office to split the allowance between the two jobs, but surely you still pay the same amount of tax overall?
Or am I missing something?