Back to the original post.
"Whose responsibility is this, and to whom should it be reported? Obviously, it's not BA's fault, but Bloody Awful Airports, but I suspect BA have more pull with them would than a passenger - unless, maybe, the HSE can be involved."
Sorry, but I think all of those placing the blame on the BAA are wrong.
I think you might well find that BA are responsible.
Why?
The bridge may be owned by the BAA but it is likely that it was a BA operative that positioned it onto the aircraft and it is also likely that the terms of operation will state that the user is responsible for ensuring that it safe before allowing passenger disembarkation/embarkation; and if not, to report the failure/hazards and prevent it's use until the engineers can isolate it.
The company responsible for the positioning of the airbridge has a duty to ensure that it is fit for use. If it is not, then they have a responsibility to report it as such and prevent its use. If the owner (BAA) then fail to take action to rectify the problem then any incident thereafter could be laid at their door.
In the way that this has been described I would tackle BA, and not BAA; AND not be out off by BA's first reaction that will be to blame the owner.
The BA operator should have noticed the wet floor and done something about it before allowing passengers to use the bridge - as a minimum - warn that the floor is wet and could be slippery. They failed to do thbis, an accident occurred, the HSE would go for BA (or whoever positioned the bridge).
Just my 10 pennyworth!
GH