I believe that the stacks continue down through the house as there are still large protruding parts of the wall where the stack would be (i.e. the rooms have not been made larger), they're covered with plaster (no gaps for fireplaces) but I assume that the brick is still there underneath.
Also I don't think that the crack continues down into the vertical part of the stack, it looks to me as though the underside of the chimney has been pulled away by gravity (probably due to weathering of the lime mortar) and is peeling away from the top.
Do you think that the central part (under the stack) is added later to support the chimney then? I assumed that this was part of the supporting wall.
It might be worth noting that this is a semi detached house and the neighbour has an identical chimney setup on the other side, so the central blob of rustic brickwork actually sits underneath 4 chimney stacks. I have no idea what this looks like from the other side.
I'm not going to fix it myself.
This would be good as it would cause the least disruption but I guess we need to get a structural engineer out to look at it first hand, fingers crossed we don't need to undertake major work to get it fixed.
I'll take a look at the weather proofing on the chimney, it might need to be improved.