There are no legal controls over the use of mobiles in any setting, childminder or nursery.
What we must have in place is a policy explaining to parents how mobile phones are used in the setting. If this is not in place then, yes, that's a safeguarding issue.
It's a waste of time demanding that a childminder or nanny does not have his or her mobile phone with them. Our LA tried it on very briefly before realising it was unworkable.
Parents need to contact us and vice versa. Ofsted demand evidence of progress (and so do many parents) and photos are the easiest way for a childminder to provide this evidence. Ofsted also inspect childminders individually (although they want to move us to Childminder Agencies and abolish that level of safeguarding because it's cheaper for them).
It comes down to trust between parents and childcarers.
If you don't trust them, you should not be using them. My parents use me because they prefer to see photos of their children enjoying their day rather than worrying that I might be sending said photos to a child porn ring.
It sounds as though there was a lot more wrong with this nursery and they probably wish the parent had never started all this.