My stepchildren regularly flew with BA from Heathrow to Newcastle to see their father and his family over the last 12 years. They started when my stepson was 5 and his sister was 8. They were well looked after on all occasions including a diversion to Edinburgh due to weather. Can't fault them. The first time was a tad stepping into the unknown for all concerned - my wife and I stayed at Heathrow much longer than we were asked to!
They still prefer BA now although they are no longer unaccompanied minors. They are comfortable with what they know.
I would recommend to any one with a child needing to travel on their own.