Nagz, I think this really depends on how much time you have before your visa expires.
For instance, if someone's meds were going to expire within 10 days then they will require you to send your passport in less than 10 days.
I had a friend who sponsored her husband from Abu Dhabi and the embassy there literally required him to submit his passport and leave to Canada within 5 days because his meds were just about to expire.
In your case however, you've done your meds recently, so i think they will give you 30 - 45 days to send your passport.
Again, though that's just my thinking... god only knows what kind of procedure they have in place for things....