Stupidity: When the army base gets overrun the girl jumps on a soldier and starts biting his neck. The woman soldier that's with him aims her gun at them but doesn't shoot, knowing full well there's no hope for the man. There is utter carnage going on all around them and instead she tries to help him and gets attacked in the same way. This could be a plot hole as well as the girl in question is the one that holds the key to survival.
Plot hole: Walking from Park Royal underground station to the base of the post office tower in central London is an achievement any day but to do it in a zombie apocalypse with no incident is a bit much to believe.