From LHR (only) BA staff will move you at LHR to another flight if the Avios bucket is open. Obviously if it opens before OLCI / 24 hours you can just do it yourself, £35 per person. If LHR does it on the day (and thus you can no longer change it) then I think it's £60 per person, and you best ask in CCR or Flounge, I think it's just the Premium team that have had the training on that one. This does not work anywhere else except for JFK and occasionally BOS, when they may do a free change in order to juggle loads between several flights. Note also that your perception as to available First seats may well not be accurate: BA will cheerfully overbook CW in order to push people into First, to give one scenario of many.