BA flights to DME are not full at all. I can't see them making any profit whatsoever since switching to LH aircraft.
Other user quoted ExpertFlyer availability but flights tomorrow are only 50%-80% full.
There are odd days when J and F on B747 is pretty good but most of the time it's either empty or op-ups. I can't remember DME being oversold in the last few months either. Well maybe someone in revenue department knows better...