I live just off Temperley Road, so south of Clapham Common in the Nightingale Triangle.
I don't notice the plane noise at all while at home, but I live in a home with double glazing throughout and good insulation. But even when I have the windows open during the day over the summer, I don't hear it at all.
In the last year, I've noticed the plane noise maybe once or twice while walking to the station, and usually I only notice the sound after I see the plane (so it is not intrusive enough on its own if that makes sense).
I do notice though that when I go to Wandsworth Common or Northcote Road area, that I have noticed the plane sound is louder than in the Nightingale Triangle.
But just to stress, the sound does not bother you unless you're looking out for it, and it is very infrequent, IMO.