This might work (agent discretion) if the segment you miss is such that you can obviously get to the destination more quickly by land, such as PHL-NYC, EWR-IAD, LHR-BHX, etc., but you would need to deal with it (stand in line?) at the airport on the day of travel where HUCA isn't a possibility if you don't like the answer. For LHR-GVA, it's not credible that you could take the train (or swim) more quickly (but if it's the last flight of the day, is there an overnight train?), so the reasonable excuse would need to be a budget carrier flight leaving soon on an airline with which BA dosn't interline, but in this case the LHR-LGW (or other airport in the region) transfer would not be a way to save time.