I would be freaked out too. I would refuse to take a shower when I know that any guy might come in too and that I might accedently stumble on them.

If I was in that situation I would try to find any public showers/baths where at least I would know there is a women only section. (Is there public baths in London?) Or I would just subscribe to a swimming pool and take my showers there without actually going to swim. Lol. I would find ways to avoid my dorm showers for sure.

Cultural thing? Hm... I do not know about that.