don't forget that (here) in Germany nudity in women's gym changing rooms can be VERY different to what i think you do in the UK.
The one i go to, for eg, there is one changing with about 20 lockers, a bench in the middle, 2 sinks and a toilet (the only ladies' that isn't off the main equipment room (where the cross trainers etc are - so it's convenient if you're undressed and then need the loo.
there is a bigger locker room with about 40 lockers, more open, and next to that the showers - 4 showers with 2 showers on each side, with walls between the showers on each side, but there are no doors or curtains they're a bit like the ones we had at school. Women will often - not all of them - strip off, take their towel to the showers, get washed, dry off and walk back to the locker area. sometimes with their towel wrapped round their hair. They might then do body lotion (i have often been sitting tying up my shoes and a woman will be there with a leg up on the bench rubbing in skin lotion. Naked as a jaybird. They may still be naked when they are drying their hair.
The women's area doesn't actually have a door (except the smaller one) but it is at the end of a corridor around a bend and men are not allowed in. There is also a sauna that has mixed and single sex days, you have to check the schedule.
so, in theory there is a strong possiblity that if someone in our town wanted, they could identify as a woman and march right on in.