What was the rule for BA lounge access in T1 when EI was part of oneworld? Could EI passengers use the international lounge in T1, or was it still totally separated at that point?

I never used the domestic part of T1 until BA moved out, so I'm not sure when the common departure area was implemented.

Presumably they can restrict access as the OW airline in question in BA and therefore as it's their lounge it's their rules (and an alternative is provided).

Just like when bmi ran the lounge, it was signed as a * Gold lounge (as was the domestic) but those travelling bmi domestic were refused from the international lounge, but the other Star Alliance lounge, not run by bmi, had to admit *G guests even on a bmi domestic flight, although some tried to 'suggest' you go to the domestic lounge.

So it seems airlines can make their own exceptions to alliance rules when it concerns their airline, but can't make exceptions about other airlines.

Another example would be AA, they can deny their own members access to the Admirals Clubs when flying domestic, but they can't change the rules for other airlines.