I would never, ever wake up a fellow traveler for something like this. Some people have rough time falling asleep on planes and once they're out, I'd assume they need it as much as I do. I would simply place the earplugs provided by BA in, and continue working/sleeping/eating etc. I always travel with my own set, as well.

For a 1.5 hour flight, I don't think I'd even have time to notice.