My On Site Guide says on p 69 ....
The OSG says all sorts of things, by no means all of which are actually requirements of BS7671. However ....
that socket outlets are "not allowed within 3 metres of Zone 1 (the edge of the bath or shower basin)", so unless you have an unusually large bathroom they would in practice be prohibited althogether.
... on this occasion, it was probably telling thee truth (at the time it was written) - although, if I recall correctly, Amd2 of BS7671:2018 reduced-the 3m to 2.5m. I presume your OSG pre-dates that change?
However, blup's post (to which I presume were responding), related to a socket in an adjacent room, not in the bathroom itself. ... but it seems that you may have noticed, because you then go on to write ...
And the controls for the towel rail should be in the same room or on the landing outside, not in a different room.
I wonder where that came from? What is the difference between an adjacent landing and an adjacent room?
Appliances such as washing machines etc need to be pulled out of the space for servicing so are not regarded as "fixed".
Well, for a start, if they are 'built in', it's often not quite as simple as just 'pulling them out'
Ovens are, ... and should have a proper separate cooker connection point.
I'm talking about ovens, not cookers, and what you are suggesting would often involve 'cutting off the plug' - which would get some people fussing (unnecessarily) about that 'invalidating the warranty' !
I really don't think one can use the fact of whether or not something is physically movable (or fixed to the fabric of the building) to determining whether or not it is part of the fixed electrical installation. And it works both ways - as I type this and look around, I can see more than one mains-powered electronic item which is mechanically fixed to the fabric of the building but which even you would probably not regard as being part of the fixed electrical installation.
I would say that this is one of those (many) situations in which common sense should really be allowed to prevail.
Kind Regards,m John