I sent off my application on 17th August, did the 3 stages over the next few months, and passed my medical on 23rd November. However, I'm not starting til July. I would say 9-10months, possibly longer, maybe shorter.
It all depends on how quickly you can get through the stages (i.e. there are only specific dates for each of the stages, it all depends whether you can get time off for them, or have to wait for another month...). Also depends if you have a medical deferral (like a friend of mine did for eyes).