Car seats designed for the British and European market do not need to be FAA approved to be used on a plane. This is an American standard that is not used in the UK/Europe.
You can use your car seat during flight providing the car seat adheres to the airlines requirements and must be used without an isofix base.
We would always recommend checking your airlines restrictions before taking your car seat with you however most airlines will allow you top check your car seat into the hold luggage free of charge alongside your cases.