My experience is that BA have an informal standby policy that, if I ask nicely, seems to work like this (also noting I am a GCH and usually hand-luggage only, no special meal, single traveller, ie very easy to move around).

If I am on any kind of ticket other than discounted economy, they will generally re-accommodate me if I ask nicely. Sometimes this is done in advance, sometimes at check-in, sometimes they send me to the lounge, and from there sometimes to the gate. If I'm on a cheapo ticket, unless there are operational reasons, the answer is always no.