The whole structure is unlike anything I've come across before, and difficult to describe: I've put some pictures at http://www.thekelleys.org.uk/edifice which might help.
The house was built in the early seventies and is brick-and-block with cavity walls.
The wall on the left of the opening is the house gable-end and contains a chimmney of pottery pipes surrounded by bricks and partly within the cavity. It has been lined with stainless steel for a later conversion to a gas boiler. The chimney stack protudes one brick length from the inside surface of the wall and starts about two metres up, where the flue pipe from the boiler used to connect with it. The wall below that is of ordinary boring cavity construction.
The wall to the right of the opening is a single thickness of blocks. It doesn't support any of the first floor structure. (the joists are front-to-back, in the same direction as this wall. What it does support is the wall above the opening. The bottom half of that is plasterboard false-work, but the top half consists of a concrete lintel and five courses of bricks. One end of the lintel is supported by the right-hand wall and the other ties into the gable-end wall at the left and to one side of the chimmney structure. There's a photo on the website looking upwards which illustrates this.
Apart from support of the chimney, the only other plausible structural use for this is to support the single first-floor joist which is positioned away from the gable-end wall to miss the chimney stack: all the other joists are supported by the wall which forms the back of the opening, and continuous over the front, five-course-and-lintel, wall.
It is not practical to remove the whole chimmney stack to roof level. What I want to do is remove the first few courses of the chimmney so that is ends a first floor level, and to remove the front and left-side walls of the "edifice". Is that likely to be safely possible? What alternative support (if any) would the chimmney need? Would the operation need building control/inspection?
The team's opinion would be very valuable in this matter......