Well as I understood the report the engines didn't respond to calls for more thrust, this could mean:
1) The engines were losing power and didn't respond to more power.
or
2) They were a little short and asked for more power, but they couldn't get any more, so the engine stayed at x power rather than lost all power.
Make sense?
Yeah. They are specifically avoiding saying that the engines shut down. I also notice that no passenger has yet mentioned that the engines or plane went quiet before touchdown. If the engines stopped, I expect the lack of noise in the cabin would have been noticed. Also, as one of the news channels has mentioned, it would be very odd for both engines to suffer mechanical failure at the same time.
It alls, to me at least, suggests that the engines were still providing power but either a) a fuel quality / quantity problem was strangling them or b) they were not receiving any instructions from the cockpit.
I wouldn't have thought fuel quality would have been the problem, on the suspicion that this would have become apparent earlier in the flight. A lack of fuel may have caused both engines to struggle to accelerate simultaneously but I am sure the crew would have been aware of a fuel shortage before that point. I'd also be surprised if the fuel feed system had no redundancy and that both engines relied on the same pump somewhere.
In short I suspect either a software problem or an electrical component failure in the cockpit / avionics bay. My prime suspect is an autopilot glitch, and it's possible perhaps that, not having much time, the pilots might not have fully disengaged the autopilot when attempting to throttle up and that the throttles were still under autopilot control. I don't know if that's possible in a BA 777, but I know some aeroplanes have autopilots that can be partially engaged, so it commands some controls, e.g. rudder, while the pilot / copilot commands the rest.
All speculation though, on my part.