The "quota" for night operations is a number for a season, but it works out at around 15 per night, which on the typical day might be 13 early arrivals between 0430 and 0600, and one or two delayed late departures. Once upon a time night operations were often freight flights operating in and out at deep night hours, but these have been squeezed out and most are now widebody early arrivals, generally from the Far East and North America.
Overnight flights from Hong Kong are commercially popular but as the performance of aircraft on the route has improved, along with progressively more direct routings across China and Russia, it is now a challenge to predict en-route winds up to 12 hours ahead, get away from Hong Kong at an appropriate late evening time, fly efficiently, and either get a pre-0600 slot or land after 0600.
Scheduled and actual can be a bit different, the quota is based on actual. So (another hypothetical example) if a BA departure at 2300 is 2 hours late getting away it can leave at 0100, but some days later an inbound approaching for 0545 may hold to restore the quota used. The quota is divided up by airline, BA are the largest user but all can apply for an appropriate share - not that there is much to go round. A landing at 0559 is a bit of a waste of a night slot, which you might need more seriously later in the season, hence why you tend to see a short lull in the final minutes.
From the back bedroom of our house, when clear, there is a distant view of the Lambourne hold, so if I am up around 0600 I often give a glance to see how much activity is there, it's a good guide to how things are going. Plenty visible (summer) or strobes going around (winter) means that the congestion has started early. Unexpectedly strong transatlantic tailwinds blowing people in early are a significant nuisance.
As Heathrow Director says, it is a longstanding myth that Heathrow is closed overnight, it is not, but there can be only a very limited number of operations.
I'm sure there's some Zealot at HACAN
who sits up every night counting them in, with one hand on the phone to the media at 0559 just in case ......