Yes it is a Chimney

Although it seems to be more like a domestic chimney rather than one associated with an industrial process.

Picture 1 is a plan view camera facing East.

Picture 2 shows where the grate is (camera facing South).

Picture 3 shows the metal of the grate and the inside of the box where the ashes would have fallen.

Is it a Chimney?

The two pictures below show the big chunky structure which stands to the East of the whitewashed toilet area. It's 5 feet square; what else could it be? We need to take the rubble off the top and look inside.