They should aim to clear the fast track lane, at least those that have been waiting, first then move to general boarding. But at both LHR and EDI, general boarding normally starts much the same time, or a little later, than fastrack. It is one of the few occasions where 'separate, but equal' often rings true.
I'm normally quite happy with BA, but the boarding process is one of the areas where they could improve. Was standing next to a couple of US road warriors, banging on how awful it is recently. I was initially dismissive, but on reflection I think most US carriers are generally better organised with boarding; well they seem to start boarding at the advertised time and seem to deal with fastrack or its equivalent first