It's true what Nox has said. I used to babysit my cousins at night when I was 13. It was considered acceptable in the 60's.
I think it does depend on the maturity of the child. However, I do not think it is responsible to leave a six your old in the charge of a 13 year old on a regular basis. It puts too much responsibility on the 13 year old who, however sensible they may be, might not be able cope in an emergency.
It is not illegal to leave a child at home alone, however, there are circumstances in which parents can be prosecuted.
http://news.bbc.co.uk/1/hi/uk/2603817.stm