There are three reasons I can think of that she wouldn't pay income tax on her wages / income at the moment.
1) Her overall wages won't be more than her yearly allowance, i.e. she won't earn more than �6475 in this tax year.
2) She has only just started work. Each month, the first �539.58 is tax free if you have a standard personal allowance or tax code. Therefore, for example if she didn't work in April and May (or up to today) she'll be allowed to take the first �1079 (or more if it's today) of her wages without getting taxed. Therefore, if she earns say �1000 per month, her first month's wage wouldn't be taxed and her second's month would be taxed less than 'normal' as the rest of her unused allowance would be added onto the tax free amount for that month, and consecutive months, until all the unused tax free allowance is used up.
3) If she were self employed, but I gather from the way you phrased your question that this isn't the case.