Yes, Swire are a UK company so there would be no nationality impediment to their taking control of BA.
Re the other comment that BA has a huge network in Asia, that is not correct. In fact it is much depleted with SEL,OSA,NGO, TPE, MNL, KUL and JKT all having being abandoned over the last 10 years. BKK is treated much as a technical rathert than commercial stop on the Australian route and so is SIN on one of the 2 daily services there. The turf has been largely vacated to the One World members QF and CX although BA makes hardly anything out of the codeshares and the joint operation with QF has virtually eliminated the BA brand in Australia.