You might be right that I was mistaken about 5:30am. Looking at the schedule I see that there are no flights before 7am from City. I must have got confused because I would have set my alarm for 5:30am - next time I will ask BD to wake me on the way back from one of his raves.

But I still maintain that the journey takes a very short time by cab early in the morning. Using public transport only takes 42 minutes, and that is without the East London Line.