I'm not sure how relevant this is but, back in the day, I was into amateur radio and there was always a discussion about antennæ and planning permission. To cut to the end, a "fixed" antenna tower over 4m high required planning permission but a "mobile" installation didn't.
Same here, and I remember such discussions and perceptions. However, although I may be wrong, I seem to recall that the situation was messy, in that there was no explicit 'rule' in any legislation or regulations, such that the 4m figure (I suspect actually not metric in those days!) was likely to vary between different Planning Authorities. In any event, anything even remotely as little as 4m would not have been of much use to me at the time!
The accepted definition of "mobile" was that it could be moved within four hours.
I don't recall that definition, but it seems pretty useless, since I'm sure that many very high towers could probably have been moved in much less than 4 hours, and those held up only by guys probably within a few minutes!
Using this definition, the Dustbuster, TV and kettle base would be defined as "mobile" whilst the central heating system would be "fixed". I don't know if that helps or just chucks another spanner in the works!
I'm not sure that it really helps, since the great majority of items of domestic (probably even commercial0 items of electrical equipment could probably be 'moved' within 4 hours. To talk about a 'central heating system' is perhaps a bit confusing, since most of it is 'plumbing', not 'electrical equipment'.
I think the only really solution is 'common sense' - and that common sense might extend to questioning the point of trying to distinguish between 'fixed' and 'mobile/portable/whatever' electrical items in the first place. A problem in terms of electrical regulations is that anything which is normally 'plugged in' could be 'unplugged' at the time of any inspection, hence any attempt to police/enforce any regulations relating to 'plugged in'items might be pretty futile (despite what Approved Doc P says!).
Ultimately, these sorts of ambiguities would be settled in a court of law where "reasonableness" and "intent" would play a part.
That's what eric always says. However, the reality is that such questions never have been, and probably never will be, tested in a Court!
... which takes us back to 'common sense'.
Kind Regards, John