Fans in bathrooms and toilets are usually organised to run on after the light is switched off - to achieve this a fan needs its own Live and Neutral to make it work and also the Switched Live (that turns the light on and off) to tell the fan to start running - a timer circuit in the fan sees to the overrun period after the light is switched off.
Your electrician will "pick up" these three wires from the most convenient place - quite probably the ceiling fitting in the toilet.
Your question does not explain the significance of the Hall Light.
Peccavi, March 2009
