I'd be curious which is actually faster: walking [assuming you only carry-on luggage] through the fly-overs or queing for taxi and then making a few circles to the MO front door?
Before they renovated the MO, I often had last minute business meetings on the second floor [famous for their high tea], and then make my way over to AE to check in and catch the train to airport. In fact, I found it silly to que for taxi, and then have driver make a turn out to the main road, then turn right, then left to AE entrance; not even sure if the meter would jump beyond starting fare?
Oh, and yes, even at mid-night, it's perfectly safe.