Might be useful to clarify how deep is the gap you're talking about. If it's 2m across by 1m down, how far back does it go? I'm guessing less than a foot. Still a reasonable amount of debris to remove, though.

If your half-house is anything like ours, it's just a gap (rather than an insulating cavity which I think tends to be a space between two sets of bricks). I think we have something similar to what you describe, though ours happens to be above the level of the loft floor, but it might be different depending on the specific house.

The rubble/builder's waste which was in there before was probably doing something towards insulation, but (and I am no expert) the best plan might be to just lay loft insulation over/into the gap if you can.