What could the owners of the gym be reasonably expected to do about a wet shower floor?
Put something on it to make it non-slip, or design it to be non-slip in the first place!
As I mentioned above, my shower tray was treacherous until I added non-slip mats.
Another example - Accy broke a hip slipping on wet decking. What could have been done...? Damn well add a non-slip surface!
I went on holiday in Devon and the accommodation had a large area of raised decking at the back of it, with a wooden ramp leading up to it. I used to wheel my bike up and down the ramp. The whole area was made safe with non-slip pads, except for the very end of the ramp. I walked onto the ramp after rain and promptly slipped over! I would have ended up in a tangled heap of man and bike at the bottom of the ramp if I hadn't managed to grab a handrail as I fell. If I had broken a hip then I definitely
would have demanded compensation. Since no harm was done I simply reported the problem to the site owner.
I went to a holiday cottage in Wales once. It was in a great location but there were 6 or 7 things wrong with the cottage, which I listed in the visitors book. My sister stayed at the cottage a few months later and all of the problems had been rectified, the main one being padding over a huge low purlin in the attic bedroom. I had smacked my head against it 3 times in a week!
It is the responsibility of the gym managers/owners to make sure that is safe to use. Shower floors becoming slippery when wet is something that could be planned for and prevented.