BA's website tells me that
Cigarette lighters cannot be taken through central security search.
They may be purchased airside and carried onto the aircraft on the person unless customers are travelling to the USA.
Cigarette lighters must not be carried onboard flights to the USA.
Cigarette lighters must not be carried in the cabin bag or checked into the hold.
A small packet of safety matches is permitted to be carried on the person but must not be put in the cabin bag.
Oh, and
Cooking Oils are also prohibited from carriage in checked or carry-on baggage.
So much for cheap olive oil...