Using a single pole three-way switch, the wiring is easy enough.
Do they make three way single pole switches? Or do you mean three gang switch?
Your fan has three terminals (plus earth if it's not double insulated): permanent live, switched live and neutral. The switched live comes from the light. This is the one that brings the fan on when the light is on. The permanent live keeps it running on its timer when the light goes off and neutral is self-explanatory.
Thats the theory but how does this arrangement fit in to what you outline next?
You insert your three-way switch in the switched live supply with its common terminal connected to the fan.
Which switched live? Where are you interrupting it?
Of the three switched terminals, one goes to the light as before (normal operation),
How?
another goes to permanent live (fan always on)
from where to where ?
??
This doesn't seem to make sense. You seem to be saying you interrupt the switched live but don't say where the switched live comes from. You don't talk about how power gets to the other 'terminals' linking wire maybe - and while you have mentioned it at the beginning the neutral seems to have got lost in the translation.
To the OP …. To achieve what you want to achieve you only need to separate out the lights and extractor fan and thus only actually need a two gang switch.
Assuming that the OP does actually mean a three (two) gang switch, then surely the best option is:
1. From the ceiling rose light bring the live, neutral and earth down to the switch - using three core & earth cable. Use brown as the live which goes into the first gang Common Terminal and the ceiling rose permanent live. The grey cable (with brown sleeving) goes into the first switch terminal L1 and the ceiling rose switched live. - This will give normal light operation with the fan inactive. The black cable (blue sleeving) is connected to the neutral at the ceiling rose and put in a terminal strip at the switch.
2. Now run an addition three core and earth cable from the light switch to the extractor fan.
3. To get the fan to work. At the switch connect a small piece of cable from the first gang common terminal to the second gang common terminal. Then the brown from the second three core cable to the second gang terminal common and at the extractor fan the brown to the permanent live. This is your permanent live. Connect the black from the second three core cable to the neutral terminal strip at the switch and the neutral at the extractor fan. This is your neutral. Take the grey from the second three core cable and sleeve it in brown and place it in the L1 terminal of the second gang at the switch and the switched live at the extractor fan. This is your switched live. The second gang at the switch will now operate the fan independently of the light. Ensure continuity of the earth.
Caution:::: The fundamental problem with this and other approaches suggested is that you do not have a means of isolating the fan for maintenance and thus you would need to interupt the second three core cable with a three pole isolator. I am also certain that most manufacturers instructions for fans say a 3Amp FCU should be used as well.
Oh and don't forget you can only do this work if you notify your Local authority building control first.