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You could do that, as long as you terminated the end of the mains cable in a sensible way, eg. mount in terminal block, and don't strip insulation back. It's slightly bodgy though; I'd want to know where it's from, and to protect others in the future. However, you can at least improve the situation just now by making it more safe...
rodabod-
Yeah, it's not ideal but the new floor is down now so finding where it goes to is a bit tricky, or would a spark be able to work it out? I was thinking to just run it into a junction box but a terminal block would be a better fit for threading it back into the staircase.
It's annoying I hadn't checked it before but I was fixing the under side of the staircase this evening and realised the wire which I had assumed it was, went a different direction and that the one in question was just hanging there.
Tenderloin
Disappears under the second set of stairs on the landing. I tried to pull it through and simply push it into the stairs but no joy.
Can't I just turn all the power off and cut it then?