For what it is worth, I got denied EI lounge access at DUB alst week on my DUB-BHX Stobart Air (BA flight nos) even with my gold card. Was told only BA LGW and LHR guests can ue the lounge.
I alos had trouble at BHX getting EI to check luggage throught to CPT as I was on two PNRs and in the end had to collect and recheck. Had a simialr probelm on the return from CPT
On the bright side, EI posted TPs and Avios within hours of the flight completion