I just wanted to share my situation as it may be somewhat helpful? Not really sure.
She will be entitled to claim the £500 maternity grant when she is 29 weeks. And is able to claim healthy start vouchers when she is 10 weeks (£3.10 per week for fruit and veg, which raises to £6.20 per week until baby is 1)
There are things such as baby bundle banks that her social worker or midwife may be able to look at and put in a referral for. And they are great! Saves a lot of money for someone who doesn't have any income. Also Facebook marketplace can be great for getting free baby items, just have to keep looking and checking every so often.
This is probably not that helpful since I'm not really sure of benefits before you're 18, but once she is 18, she'll be able to claim universal credit and the child aspect of universal credit too. And once baby is born, she'll also get child benefit (£21.05).
I know a 'termination' may seem like the best thing from an outsider perspective, but it's ultimately her choice and if she is going to keep the baby then the best thing for everyone to do it support her in doing so 
Babies are only as expensive as you make them. Other than the basics, (nappies, toiletries, somewhere to sleep, clothes, food, and lots of love), they don't really need an awful lot of 'things', that's where the expenses are which can make having a baby seem like a LOT of money. By all means, it's not cheap and is a serious decision to make, however it doesn't have to be expensive if you get what I mean. For example, babies don't 'need' a sleepyhead (over £100), a fancy play gym (£50), or a bouncer/rocket/swing thing (can be up to £200).
I'm almost 18 and expecting my first baby in a few months time, I'm still living at home with my parents (I know my situation is completely different to the young lady you mentioned). I have a personal adviser with social services who has very kindly made a referral to a baby bundles bank. So far I've managed to get a play gym, baby bouncer, clothes for the first 3 months, lots of nappies, wipes, toiletries, a mini cot, and other bits (all got myself, not from the bundles bank, but looking on Facebook marketplace and also buying a pack of nappies every-time I'm in the supermarket).
I also have depression, anxiety and an eating disorder that I'm in recovery of, currently in the process of applying for pip too. I'm in no way 'mature' but knowing that it is my responsibility to care for this little person that I'm growing, and it's made me 'mature' a lot! I also don't have a job currently, but am saving any penny I can 
I know it may not seem like she's mature enough, but having a baby will make her grow up an awful lot!
I don't know exactly what I was getting at, but I hope that maybe what I put was somewhat helpful 