After clearing the top of the chimney out, I discovered why I had been unable to dislodge the bricks from below: when the top bit of the chimney was rebuilt using horrible modern bricks, the builders (presumably the same ones who backfilled the lower part of the flue with rubble) put in a weird constricted bit between the lower section of flue and the new upper one. The flue is larger both above and below the constriction. I'm really not sure what the point of it is, and it will need to be removed if the flue is to be made usable again (either for the Rayburn flue or to reinstate the open fire in the bedroom).
This photo was taken looking down into the top of the small-bedroom half of the chimney:
The gardening hoe is there because I was using it as a tool to push assorted detritus down the flue from the top. It should also give you an idea of the size of the constriction.
While I was up on the chimney with a camera I took the opportunity to record a rather poor quality wobbly video showing the view around the house (not recommended for viewers with vertigo or motion sickness! ;)