Can I install a washing machine in a bathroom?

Electrically speaking there’s no issue with a suitably rated FCU in zone 2, like you’ve pointed out the debate is whether the washing machine is suitable for the external influences. Only the manafacturer can give you this, minimum of IP44.

If you are installing in a zoned area even zone two the chances are the machine is not suitable. In the continent this is common but the rules are very different. Also where is you power coming from hopefully not a power socket in the bathroom and running a power lead is not recommended even though in Australia and America you are allowed to fit sockets in the bathroom even above a sink! So generally unless you have a big bathroom best avoid and put it elsewhere.

So long as you’re RCD protected and not using a socket outlet it will be fine.