Is it an ex-UK ticket? Are you sure it allows date changes on the first sector? Many cheapies are date-changeable on all except the first sector.

And are you going to try to get on anything tonight? If it's an ex-UK ticket from a travel agent, your first port of call should really be that travel agent.

And may I ask whether it's the sort of family crisis for which you could get documentary evidence, eg a doctor's letter or something like that? An emergency of that nature of which you can get evidence may get you more help, favours and waivers than other types of crisis.