Originally Posted by
MikeWhiskey
Am assuming the EI segment is a codeshare and has a BA flt number? That being the case you'll be checking in with BA (or it's agent/handler, which may well be EI at Cork) for a BA flight ORK-LHR-HKG and should receive both boarding cards and have your bag checked all the way to HKG.
BA doesn't operate ORK-LHR. Therefore OP's flight, whether booked under a BA or EI flight number, will be operated by EI.
You always check in at the airport of departure with the
operating carrier of the flight. Therefore OP would go to the EI (or EI handler's) check-in desk at ORK - not BA's.
Whether that desk can provide the onward BA boarding pass I don't know, but as Tobias says OP should be able to retrieve this online.