It's not hard - the dispatcher/turn-round co-ordinator knows the figures as soon as the doors are closed. However, BA's policy is to use a set of centralised load control centres (I think there are 5 - New York, Joburg, Hong Kong, Berlin and London) to finalise the churning of the figures the dispatcher has in their hand. This saves the expense and licensing difficulties of keeping several hundred individuals around the world (and not necessarily BA employees) up to speed on Load & Balance calculations.
It also frees up the dispatcher to concentrate on the stuff they can affect, such as pax/freight/catering/fuel loading and helps punctuality.
Of course, the downside is that the figures have to be sent from the outstations to the regional centres, and Murphy's Law being what it is, delays can occur. All it needs is the dispatcher to be stuck crossing a taxiway and unable to reach a fax/telex and the system falls down. Some stations are more prone to this than others (maybe at CPT the dispatcher has a long way to travel to send figures).
However (and it is enormously embarrassing when it happens) it doesn't happen all the time - and those stations where it does can easily be identified and (hopefully) actions taken.
Hope that clears things up.