On a recent flight we tried to use a child safety seat, specifically the
Chicco KeyFit 30 (without the optional "base" for a car), which faces backwards and which is secured by passing the standard airline seat belt (or car seatbelt, in another context) through some hooks on the top of the seat -- not through the back like many infant/child seats.
BA's cabin crew said that the seat couldn't be used if it wasn't installed facing forwards, and were perplexed that the seatbelt didn't attach through the back of the infant seat.
By contrast, we've never had a problem on either AA (many flights) or LY (two flights) using the seat facing backwards and attaching it with the standard airline seatbelt.
I didn't press the point because we had lots of space (on BA, we were traveling in J and ended up with a blue infant reclining seat provided by BA which the crew installed on the bassinet tray, and three CW seats between two adults and the infant -- which made for a tremendously comfortable flight. Also, the crew were incredibly kind and helpful in general. So there was no reason to insist on using the infant seat itself.
I did wonder, however, whether for potential future flights in economy (and for other passengers) on BA it might be helpful to clarify whether the crew made the right call.
AA note
here in their advice about infant and child seats that:
Acceptable safety seats
Most safety seats that are approved for use in motor vehicles are acceptable for use in aircraft. The seat must have a solid back and seat, restraint straps installed to securely hold the child and a label indicating approval for use on an aircraft.
The label may include:
These notes: “This child restraint system conforms to all Federal Motor Vehicle Safety Standards” and “this restraint is certified for use in motor vehicles and aircrafts” or “this restraint is certified for use in motor vehicles and aircraft.”
Approval of a foreign government or a label showing that the seat was manufactured under the standards of the United Nations.
Safety seat requirements
The safety seat can't be used in an exit row or in the rows on either side of an exit row.
Install the seat in the direction appropriate for the size of the child and according to the instructions on the label.
The child must remain in the safety seat with the harness fastened during taxi, takeoff, landing and whenever the “fasten seatbelt” sign is on.
To carry on a safety seat, you must have bought a seat for the child, or a seat must be available next to you. If an unoccupied, adjoining seat is not available, the gate agent will check the safety seat to your final destination.
Note the section I've bolded...