Cathay is reportedly on the lookout for secondhard 744s as well, so BA's RR powered aircraft would probably be a good place to start; it wants to convert some of its early 744s to freighters (someone - can't remember who - is starting a 744 pax-to-cargo conversion project; I think it's Singapore Aerospace) as well as add capacity to its pax routes.
I fully expect BA to reduce its 744 fleet, as it can, but unfortunately, there are not too many takers for them and rather than trying to fire-sell them, which is doesn't need to do - it can keep them going. Another problem is a replacement. The 773 seems like a logical choice, but the ER is only available with GE engines; the best option might be an increased gross weight RR model, but that would still be relatively short legged and certainly would not be able to do n/s from NRT, SIN, BKK, HKG, which would be a requirement. Might they consider the ER? Who knows; they have GE90 experience anyway, so it can't be ruled out. Surely more likely than 340-600s anyway.
BA has said it doesn't want the 380, but I think events will probably force its hand. Besides which, in all fairness to BA, it's been a standard setter for the latest F and J class products, which cuts down on aircraft capacity because of the space taken up, so a 380 in BA configuration might not seat more than 400-450 pax.