I live in London, I have worked in London all my life, my kids grew up in London. I go out socialising across central and many areas of London. I worked in a job that meant travelling home late at night.
I do my best but I can't help it, most of this makes me roll my eyes.
London is full of young people making their way to and from school on buses and trains from age 11. Teens out and about independently. Women (yes, women!) coming home after work in the dark, women of all ages going out with friends, shopping, bars, theatres, etc - and getting the NIGHT BUS home.
It is a normal city where the vastest majority of people go about in absolute safety. I know that phone snatching has become more common - I don't know ANYONE who has had their phone snatched. I know that people have, it's always good to be aware, but really, can we get some perspective.
And - there won't be a member of staff to ask what tube platform you need. The signs and diagrams are clear and massive. If they are a bit confused on the tube - ask a Londoner - we are generally really helpful to visitors. (You might have seen us helping people with buggies or heavy cases on tube steps)
Your granddaughters will have an amazing time.
My Dc and a few friends went inter-railing for 4 weeks across Europe aged 17. I can't pretend I wasn't a a bit apprehensive, we always are when we see wings being spread. But I didn't do any of this phone tracking etc. And don't ask for constant 'reassuring' updates. If they get too busy and excited to update, or tiredness and activity causes them to go t bed without messaging all it does is cause needless panic. A few stupid selfies and sightseeing pics is great!