The Horniman Museum is in Sydenham/Forest Gate and probably too far off for someone who needs to get back to St Pancras IMO.
There's plenty much closer to hand.
That's Forest
Hill, t'other direction, but is indeed a bit of a trek (train from London Bridge). For Londoner's though, it's a splendidly eccentric collection ranging from totem poles, through musical instruments, to fish. Heartily recommended, and when you are done, go to Crystal Palace park and see the wrongosaurs. Then eat some cake. A good day.