Well, my colleagues and I are not CRB cleared, which is a requirement if in charge of minors, I believe. Also, we are not "in loco parentis", even if we are on the train! (Sorry, I couldn't resist it, it seemed quite apt!)
Further to this, the responsibility for a child rests with the parents. Unless an organisation specifically takes responsibility for a child (eg school), then the child remains the parents responsibility. Indeed, the Dept of Children Schools and Families are quite specific that if a child leaves a school (who do have a duty of care) during breaks, then the duty of care reverts from the school to the parent.
see
http://www.lifedownloaded.com/blog/in-loco-parentis/
Given that the child's school (who have formally accepted a duty of care) can wash their hands of the child if they are not on the premises even during school hours, then I seriously doubt that a TOC can be held to be in loco parentis on such a casual basis as the parent buying a child ticket and sticking little Johnny or Jane on the train with instructions to get off two hours later, Uncle Frank will be there waiting for them.
As I said, if any parent asks me to look after them during the journey, I will of course be aware of the child, but I will not take over responsibility for the child from the parent, and I make that plain to them. I am not carrying the can when little Johnny or Jane ends up spilling a hot drink on themselves, or has Gary Glitter sit down in the seat beside them.
The official position of FGW is
At what age can children travel on your trains unaccompanied by an adult?
There is no required age set down by First Great Western.
The responsibility and decision lies with the parent or guardian of the child.
However we do advise that staff will not be able to watch over any child travelling alone.
http://www.firstgreatwestern.co.uk/Content.aspx?id=3633