As to your ability and if you can I don't know but I could wire up a fan in that manor.
A number of points though.
1) To comply with building regulations if that is why you are fitting fan then only if there is no or little outside light would it comply as if well lit then people may not use the light.
2) Odd but a simple pneumatic timer switch to power fan does comply even though nothing forces user to switch on the fan.
3) The fan to comply also needs a run on time and often to get this the fan has a built in timer so it requires two line feeds one to start it and one to allow it to continue to run.
4) Fans do fail and when they do they can fail short circuit so there is a need to be able to isolate the fan when it fails.
5) There are two common ways to power fan. One is to use a three pole isolator and take direct from the light but this means the fan has same fuse as lights. The second is to use a double pole switch and a fused connection unit this method allows a smaller fuse to be fitted and many fan manufactures recommend a 3 amp fuse and this is really only way if you want to fuse down. There has been some debate as to if when powered of the lights a 3A fuse is really required and phoning manufactures has resulted in different advice even for same fan.
6) The work will come under Part P.
7) Because it is an addition it will need RCD protecting this could be done by using a RCD FCU but would then mean light switch would need to be double pole and second method used.
Much would depend on why you want to install an fan. And if one wanted to be pedantic one could say it would have to have a heat exchanger to comply with all building regulations. So if I had to fit one I would first check with LABC what they will accept before buying anything.
In fact it is so much expense to pay council for Part P likely just same price to not DIY and get an electrician to fit it.
I do have wiring diagrams but pictures and links not allowed on this site.
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