I think it's ok, but depends on the child.
I had rules, though and you MUST sit down and explain what to do in an emergency first.
I sat down with dd and asked what she thought she should do in an emergency (fire/accident etc). She thought she would phone me. I explained although I, of course, want to be the first to know, she has to first call the emergency services if necessary (I would rather they were called out than she spent time calling me while she had blood gushing/a fire had started behind the telly) or alert a neighbour she trusts (next door neighbour is a friend and on speed dial on land line), then call me.
My rules are
No boiling kettle
No sharp knives
No answering phonecalls to numbers we don't know
No answering the door (neighbours and friends/family know to call first)
No friends over
No cooking except toaster
No fire of any description!
This may sound harsh but safety first. She can now do most of the above except the phone call/door answering. She always adhered to the rules as she loved having the place to herself!
I had to leave dd sometimes at just turned 11 and she is now 13 and will watch her wee sister aged 2 while I go to the shops etc, but never for more than an hour and I trust her implicitly.
I have friends who would never leave their kids alone at 11 tho. Horses for courses and aw that...