After removing all the plasterboard from the ceiling and walls in this landing area a few months ago, we were left with posts exposed where this wall was. These wobbled like hell, so were clearly not playing a structural role, so yesterday I took them out.
This has opened up the area between the staircases, and now avoids the need to step over the beam that was at floor level (see photos below) when making one's way to the next level. As it turns out, this beam was simply resting on the floorboards, so it looks like it could have been a later addition, probably so a door could be built in.
Of course, the posts and beam haven't completely bitten the dust. They've gone into storage in the barn with many other timbers and will probably get reused for other projects. Some day...