OP is your DUB - LHR sector on EI metal but BA flight number by any chance? If so then the above rule shown by @
irishguy28 might be applicable (and yes also you could chance your arm at the lounge you never know, might get lucky).
As far as the waiting for the membership card and luggage tags it seems variable but certainly a month (or 2) waiting is not uncommon based on anecdotal evidence of others, personally mine have always arrived within a couple weeks.