Does a child need written consent to travel without parents?
It depends on the age of your daughter and the airline she is travelling with. A number of airlines do have an unaccompanied minor policy, by which children can travel alone on aeroplanes under the eye of cabin staff. Once she reaches the airport she will be shown through security and immigration on both sides by a member of staff, but I imagine the airport will charge for these services. With British Airways, I believe that if a child is below the age of 12 and isn’t accompanied by anyone 16 or over then the airline must be informed. However these services and regulations may differ between different airlines, so to save yourself hassle later I would call them up and check.
