Good morning! Yes, in the last few years before I retired I managed a probation hostel for female offenders, many of whom committed benefit fraud as well as serious offences for which they had been imprisoned. We had regular dialogue with the benefits agency when we were aware of ongoing fraud, and our information was always acted upon. The result for the offenders was that they would be called in to reassess their claim, often interviewed under caution, and the outcome was very mixed. Some would be required to repay a small amount each week, some had benefits stopped whilst the claim was investigated, a couple were prosecuted for benefit fraud, and others had no penalty, other than an invitation to renew their efforts to seek work. It all depends on what information is given and what can be proved, and what entitlements they legally have.
In the case of your daughter nannym I would take into account the fact she is a single parent and how confident she is about the relationship she is in, because many young single parents fear losing an income if their 'partner' is not reliable. Many female offenders commit benefit fraud because of their experience of having their income disrupted. She may have lost confidence in her ability to get through a job interview, and so work for cash in hand. She could be entitled to housing benefit even if she is working - it all depends how much she is earning. Many women in this situation earn a pittance and don't realise they could be claiming benefits and working perfectly legally.
Or....she could just be greedy and lazy, and have got complacent about this lifestyle that needs little effort to keep the money rolling in. You will know whether she is one or the other, or somewhere in between. If she is prosecuted for benefit fraud, she will be required to repay some or all, if her income allows, and is likely to receive a sentence of Community Service/Unpaid Work, sometimes with probation supervision attached. Having a child doesn't make her immune from prison, but she is unlikely to be imprisoned for a first offence, unless we are talking tens of thousands. Ironically, prosecution for benefit fraud often has such a devastating effect on young women that they sink further into that benefits rut and continue to need to claim.
Finally, I would say think about the consequences of informing on her - will she know it was you, will that affect contact with your grandchild, what other repercussions could there be? If you do it anonymously, will her life be so seriously affected that your relationship will flounder anyway? Lots to think about. Can you help her to get out of the benefits rut and motivate her to get back on her own two feet? Hope that helps.