I think the biggest cause of this was the promoters underestimating the popularity of Asake. Afrobeats is a huge global phenomenon, Asake one of the biggest stars at the moment, a rising global superstar. His shows are a spectacle - he's bought a goat on stage, he's handed out cash to the audience, he's in his prime as a performer, his album from this year has been turning up on album of the year lists. The Acadamy sold out three nights in minutes. He could've probably filled a venue like Wembley Arena or the O2. This was the last chance to see him at this point in his career in a venue the size of the Academy.
Sure, the Academy has sold out before, but once tickets are sold out there's no way of knowing how many people still want to go or how desperate they are to go. LCD Soundsystem selling out the Academy is an order of magnitude below Asake's current popularity. This is why some fans were predicting crowds before the event.
According to some BBC coverage I saw someone tweeted early in the evening that it was quiet outside. If people are desperate to go that's clear an invitation to go down on the off chance you can get in. Just because an event has sold out doesn't mean the venue is full. You often don't know how full a place is til you get inside. Soon thousands of people gathered and the crush formed. Once a big crowd has formed individual actions don't much count. Did a handful of people act like arseholes? Naturally. We're they the cause of the crush? No.
Could this have been forseen when the show was booked? Possibly not. Should crowd control outside the Acadamy have been put in place beforehand? In retrospect, definitely. The question is, how predictable to the authorities was this, as opposed to a handful of fans who are really engaged with Asake. Should they, could they have known this would happen and acted on it?