Not to worry. The procedure, if his death occurs, has been practiced many times. There's standard operating procedures about who is notified in what order and in which countries and at what timings.
All major media (BBC, CBC here, other national news in other commonwealth countries) have the same type books on timings for announcement, blackout (mourning) periods, music selections, order of music, etc.
Britain can expect the BBC to be out for days except for news when one of then goes.