Bathroom mirror light from power circuit

[wolverhampton]

There is no access to connect a bathroom mirror light from the lighting circuit.

Above where I have my mirror is obviously the ceiling and immediately above the ceiling is a bedroom with a power circuit outlet just above the skirting. It is inches away. Can I connect the mirror light through a suitable pull cord switch mounted on the ceiling hard wired to the inside of this power source?

 

[Spark123]

Are all circuits in the bathroom protected by an RCD? Is this socket circuit also protected by an RCD? Is supplementary bonding in place?
You wouldn't connect it directly to a socket circuit, it depends on the type of circuit as to whether or not you can spur from it. If the socket you wish to spur from is on a ring circuit (not a spur) or it is a radial circuit then it may be possible to place a fused spur (with 3A fuse) next to the socket and run the light and switch from that.