If you can maintain the 2400 points required to make status with EI, keep with EI, you can earn points on BA if you have reached Gold status, so if you are Gold and close to Prestige (4800) keep going as if you have a flight EI onto BA via LHR sold by BA at Prestige level you can use the lounge in LHR
The lounge, check in, priority security at DUB and LHR with EI are good and you will get a lot of use out of them
BA won't give tier points on EI flights unless you purchased under a BA code, and its nearly always cheaper buy a single ticket with EI than BA on Dublin - London. 2 round trips on BA long haul is not going to get you even close to BAEC bronze unless you are paying for WTP or CW