Why were they on 'B' is not the question here, they were.. I agree the signage is bad, well non existent, but the crew will have had access to updated charts and will no doubt have significant African operational experience, with all the issues that involves.
If they were parked on an unfamiliar stand/area of the apron then one would think that more than just a cursory review of the unfamiliar taxi route would have been completed in the pre-flight briefing. As has been mentioned a thorough monotone line by line briefing of the EXPECTED taxi out route can be of limited benefit (especially in China!) as the route issued can and will often change depending on other traffic movements which by it's nature is dynamic, not to mention other variable factors. What has undoubtably happened here is that the crew temporarily lost spatial awareness - we have all been there.
What some airlines advocate (not sure on BA's stance) is a running or progressive taxi brief between the crew as the aircraft taxi's, for example - PM "taxing on A, cleared onto C which is 2nd left, a 90 degree turn - do you agree?" This cheks crew confirmation, understanding and highlights any disagreement/ambiguities in their mental models. If this had of taken place, they MAY have picked up the pitfall of M leading on from B.. Distractions can be a huge issue both taxing and in the air and may have played a part even if it occurred for just a few seconds at the wrong time (cabin crew calling with secure, RT call, FMC input, Final Figures, ill timed conversation etc).
IMHO they didn't slow down or stop and check with ATC on their position as in their minds they were taxing down B expecting signage on the left for the active runway holding point. I imagine the penny only dropped when somebody heard a nasty noise or more lightly yaw and extra thrust needed to continue taxing..
As has been said, all of us (private and professional) make mistakes of differing magnitude on each and every flight, most days it is an incorrect freq selected or minor SOP slip, much less frequently it is excepting an incorrect clearance, selecting an incorrect speed or perhaps taking the wrong taxi link onto a main taxiway with little consequence, but on this day for this crew the holes lined up and they hit a building at some speed.
I look forward to reading the AAIB report and learning of the causal factors which I am sure we can all learn from. Assuming they were not negligent (sending SMS, laughing/joking, intoxicated etc) then it was a genuine honest mistake. Punishment enough will be to know they have written of one of the companies aircraft and further that everybody in the airline will know who was responsible (I suspect there are no secrets, even in a huge airline such as BA). I hope BA deal with it in a mature, diplimatic and professional way. I do feel sorry for the chaps but also it was very lucky that wasn't an office full of people in the 1st floor of the building on that night.