2-3 weeks, my goodness that was quick. I waited 3 months. It totally does vary. I've seen people rush through the process faster than me (but none slower than me). It's all just luck. BA are very disorganised. I've seen one guy who sent back his medical form a week after me but got granted final board a week before me. There's no logic!
TB
BTW. Good luck with your application, but if you don't get it, make sure you get feedback from BA as to why (if you fail at FB stage). There seems to be a rumour that BA do not give feedback - that's not true, they just make it difficult for you. Persevere, as the feedback you'll eventually get should be detailed and extremely useful should you decide to try again.