I have never done it at night however it is a short and straight forward route. It isn’t the most pleasant route but is lit and there are pavements. Just be a little cautious with traffic. As you come through the barriers from the tube head to the exit on the left. Then head for the pedestrian bridge in front of you and cross it. Then follow this road round to the right. There are a few entrances to car parks etc you need to cross but pay attention and you will be fine. You can take a look at most of the route on Google Street View. 6 mins is how long it takes for an average to slow walker, if you walk quickly it will be less.

One tip if you are taking an early morning flight the next day is to check the times of the first few tubes on the TfL website as they start around 5am but are only every ten minutes.