No ID needed by BA, except if checking luggage when a BAEC card will suffice.

Do be aware that the Police at either end have been known to ask for photographic ID on occasions. Police in NI can ask for photo ID under anti-terrorist legislation though it's been ages since I've been asked even when flying. I have seen police monitoring inbound flights and they even have podiums in arrivals.

Occasionally on departure from Belfast the Home Office perform checks on those departing, even when there are only domestics leaving. This I presume is due to the open land border with the Republic acting as a potentially unguarded entry point to GB.