I have to extract from two bathrooms and one shower cubicle and can only exit through the roof.
Is there a system where I can install one main fan in the loft for all three rooms and duct out of one roof pipe?
Yes, you can install a central fan with appropriate ducting but you may be looking at a lot more in cost terms than you might want to shell out. Search the internet, UK sites, for domestic ventilation systems. But, considering that it's unlikely you'll be using all three bathrooms at maximum water vapour generating capacity at the same time it might be much more simple to go with three separate systems.
Think about it; one unit serving three locations would probably need as much ducting as three separate units. You would also need three devices in parallel to operate the unit, either switches or humidistats. And if the fan goes down you lose ventilation in all three rooms.
Have you considered three separate fans, with four-inch ducting from each going to a central manifold with a single six-inch outlet? You might also want to ask your question on the plumbing and heating forum. Hope that helps.