You could try and jump.
Nah, just kidding. . . have you been inside?
You can go East, right? What other direction is implied?
Down.
It's too tight a fit.
You can only go down if you are empty handed.
You'll need a light source, once you go down.
Drop the lamp (or for that matter, all) down the fireplace. Then enter the fireplace. Then go down.