Yes, you can, and customs for checked baggage will be cleared in EDI (even though your baggage will be inter-mingled with domestic passengers who don't need to clear customs). The UK has an interesting system for transit: at all UK airports you must clear immigration at the first airport (LHR in your example) and you must also declare any dutiable items in hand baggage at that time. At all airports except LHR/LGW you must also clear customs with your checked baggage and recheck on the domestic UK flight. At LHR/LGW you do not clear customs with your checked baggage and you do not recheck your checked baggage (you never see it at LHR/LGW, it is transferred to your connecting flight most of the time, the rest of the time it goes to Lagos). Instead the final part of your international arrivals processing is done at your final destination airport (EDI in your example). The baggage tags on your luggage indicate that it requires customs clearance and it will be segregated upon arrival (each airport does this differently, how EDI does it I don't know, but often it means your bag will take an hour or two to arrive, after all the other bags). A quaint system (I suppose it is intended to justify having customs agents at airports that don't have any international flights, as all UK airports have to be ready to process customs for inbound international pax).