BA use Sennheiser ANR of some sort which are (certainly on the 'bus) hardwired to the aircraft so you're unlikely to be able to use your own. Having said that, I flew with a guy a while ago on the Triple (where the headsets aren't hardwired) who had his own preferred set (non-Sennheiser, non-ANR) which worked fine....
Whether or not it's allowed is a different question.
