Help me find an AA Light/Lantern for Bathroom use

Behind the grate of the extractor fan is there an electric outlet, like we usually have in the states, where we can replace the fan by unplugging it and removing a couple of screws or bolts?

It’s not my bathroom lol, and I don’t know about a razor socket. As Carpentryhero says, in the UK building regs ensure that there must NOT be standard electrical sockets. 240v AC, dampness and hairdriers do not mix. Some (isolated) protected razor/toothbrush sockets are allowed, but these are not the standard 3 pinned electrical sockets.

Yes it is similar here with the protected sockets.

In general, the US requires outlets in bathroom (also unfinished basements, garage outlets, kitchen counter outlets, outdoor, etc) to be GFCI outlets. They accept the same plugs as any other normal outlet in the house. Electrical outlets in bedrooms are standard outlets, but have to be protected by Arc Fault circuit breakers instead of a normal circuit breaker.

Their exhaust fans are hard wired? In the US we could plug in a simple timer inside the exhaust fan box that would keep the fan off at night.
!!

I solved the bathroom problem for all mankind: Nichia 219 Motion Sensitive Piss Light

Neat, very neat.

I guess I should really have a look at the fan before finally deciding what to do.