Don’t work for BA, but I would say that you were just introduced to the world of Derated Takeoffs.......
Primarily these are done to increase engine life by reducing the stresses on takeoff, the aircraft didn’t need all of the 13,000 feet for takeoff, therefore the excess runway length is traded for a power reduction.
Getting to see the runway end lights is quite normal, perfectly legal and safe
As for hows it done, a takeoff analysis would show the crew how much weight they could takeoff with if:
1: They used a fixed derated engine, 10% or 20% less than the installed engine.
2: The temperature was hotter than it actually was. This hotter temperature is then used, this is called the "assumed temperature" method of reducing thrust.
The crew would input the weight, engine rating and temperature into the FMS, which in turn would provide speeds and power settings. Combining both methods allows us to reduce engine thrust by up to 45% if the conditions are suitable.
Finally remember that your perspective from a passenger window is completely different from that of the crew who know exactly that they have "planned" to do.
Cheers.
Mutt.