The other thing to remember is that just because there are no seats for sale, or you've been told the flight is oversold, doesn't mean there won't be seats for those who turn up.
One of BA's great commercial strengths is its sales history and its link into the pricing structure. Run through a system called COBRA (Capacity Optimisation Brings Revenue Advantage), it sits all day ploughing through various permutations with tweaks from Revenue Management being applied right up until departure.
The end result is that MOST of the time, a flight is oversold but leaves with seats free. If memory serves, even the final few weeks' of Concorde flights were oversold!