As someone who is due to fly today on a B777 (not BA) I am interested in the following:
The fact that the crew have been publicly exposed to the media would indicate that there is no question of operator error as an immediate cause of this accident. This means that, presumably, a system failure is still a possibility. In this case I am wondering why B777s are still being permitted to fly whilst there is any doubt as to the actual cause.
A good question.
AFAIK, the "authorities" look at the severity of a failure but also the probability of it recurring. As the 777 has been flying for over a decade with nothing like this (simultaneous failure of two supposedly separate systems) being reported, they probably take the view that it is unlikely to happen again in the time it takes to do a more detailed investigation (a month, maybe).
There are inevitable commercial aspects: there is no such thing as complete safety, only a probability of success (or failure); grounding every 777 in the world (I believe 6-700 are flying now) might not produce a justifiable increase in flight safety, just major inconvenience and financial loss to airlines and their customers.