Single-Prop Pilot, not a Scientist...
...but to me, reading the report, it seems that the low volume of fuel in the centre tank remained there for the majority of the aircraft's flight, and especially existed when the aircraft ventured through the coldest portion of the flight. All the air in the central tank would act as a wonderful insulator to the warmth of the cabin above, but being quite close to the skin of the aircraft, would have been especially cold (gravity pulling the fuel to the bottom of the plane and all).
Then they scrubbed the centre tank contents into the respective left and right-hand main tanks, pumping whatever ice-crystals had formed in the fuel with them. Being uniformly spread in the centre tank, the main tanks are now uniformly contaminated.
A descent from FL400 doesn't require a significant level of thrust, and so the fuel flow would not have been excessive enough to disrupt the suspended crystals. However, the approach to LHR requires the constant changing of the thrust (at times to high levels), which would have started to clog up the filters. And if you've seen what happens to your plug-hole when you get hair clogged up, you'll appreciate that ice clogging filters will only cause more ice to stick to it as it passes. In fact, an increased demand for fuel will actually causes more ice crystals to pass near the filters. Some of these will naturally join with those already on the filter. In a twist of irony, demanding more fuel may actually speed the problem rather than solve it.
Why did the engines fail around the same time, because both tanks would have been uniformly contaminated by the central tank, and layman math would suggest 7 seconds difference between failures would be perfectly reasonable.
But that's just my 2 inches of manifold pressure!