[Stooky Bill]

This is the clip. I'm not sure if anyone recognises the notification sound as being normal, it takes a couple moments for someone to switch off. Around 30 seconds later, you can hear someone walking onto the set, and then - more audibly - whisper something to Nicholas Witchell, while Huw is speaking.  I can't make out the specific words but the sentence does seem to end in "fallen". Theoretically, it doesn't make sense why the news has to be orally delivered to the Royal Correspondent, but that alternatively would be intentionally leaving the control room in the dark - therefore wanting to avoid using the earpiece.

The whole 'London Bridge has Fallen' is very overstated, it certainly wouldn't be used to inform a news presenter. They'd be told directly 

I don't think 'Operation London Bridge' is even a thing at the BBC, its a codeword for one of the plans for a royal death and the BBC and others  will know what it (and the other Operations such as Lion, Unicorn, Marquee etc) contains, but it's a codeword for the Palace and the Government