Don't count on it - BA's general policy on el-cheapo tickets (as I have learnt on more than one occasion) is that you fly on the plane you're booked on. If they let people stand by for earlier flights there would really be no reason for people to buy flexible tickets.

The expection is if the flight you are booked on is overbooked and it's to BA's advantage to get you out of the way on an earlier flight.