Originally Posted by
fruitcage
When the wheels leave the ground.
Sometimes after that if the seat is defective.
Few things in aviation are guaranteed, but having checked in with a seat allocated against your name is a very good start, particularly if you have status, but even more so if you are on carriage (have a connection) and more so still if you are not on a 125 or Joint Business ticket - BA are reluctant to muck up other airlines' tickets.
Statistically you are far, far more likely to be upgraded.