Originally Posted by
Tartegnin
OP Here - OK, I stand down from my initial disbelief (but not my annoyance).
[SNIP]
Of course, I should have researched smarter on FlyerTalk and better prepared myself

What hasn't been mentioned thus far is that while EI has been purchased by IAG and thus has the same parent as BA, and notwithstanding you were on a codeshared flight, EI has not yet rejoined OneWorld so the lounge access provisions of the alliance do not yet apply; to all intents and purposes you were travelling on separate airlines so were correctly directed to the DAA lounge.
Glad you enjoyed your flight in any case!