A solicitor will do one of two things. One, either sue the firm for damages or compensation, or two, which seems the more likely given what you have said, say they can do nothing because there was no actual fault on their part.
You've reported and recorded it, and as such anything that crops up later as a result could be legally attributed to that event. By that I mean if you have problems and you think they are because of this fall, have time off or have to see a doctor etc, then they'll find it harder to discipline or dismiss BECAUSE it was recorded. Of course, the problem here is proving a connection if it came to it. Personally, i'd just accept it was your own fault and see a doctor if I needed to,