Why does she already do a tax return? You normally only do one if you're self employed or if you have to repay some child tax credit.
If she's already doing a return, it would be foolish of her not to include it if it's above the £1,000 threshold.
It is possible that HMRC will pick it up because they do receive reports from banks, but at the levels of income involved, it is pretty unlikely that they will do so.
I have worked in accountancy for over 25 years and have not been involved in any tax enquiries for lower earning clients. The tax enquiries tend to come with higher earners, or those that have done something more major, like "forgetting" to include rental income on their property in their tax returns. In that case, HMRC did do a cross referencing of land registry details for any multiple home owners to catch people out but gave an amnesty against any penalties for people to own up.
Even if someone reported her, I don't think she'd be anywhere near the top of HMRC's priority list. At around £100 a week, let's say she earns £5k a year. She'd be generating a tax bill of up to £2k on it if she's a higher rate tax payer (but could reduce it by accounting for eligible costs).
As much as £2k is probably a lot to her, I know of people that have racked up debts in the 10's of thousands with HMRC and all they've done for years is send a reminder letter that it needs paying.
Is it right? No, but I expect she'll get away with it just fine.