I was living in Belgium at the time and could pick up the BBC on TV there. Had been out clubbing the night before, came home in a somewhat confused state at 7 or 8 in the morning, and couldn't figure out why Peter Sissons was on every channel. I remember that it felt like he was talking for well over an hour before he actually spat it out. (I also remember being really annoyed because there was something I had been looking forward to watching later that day on BBC2 and I ended up having to watch Vergeet je tandenborstel niet re-runs on VT4 instead.)
The strangest part of the entire thing was watching the televised reaction of people in the UK over the following weeks. My girlfriend at the time was English, most of our friends in Belgium were British or Irish, and none of us could figure out where all this public mourning was coming from. It didn't seem in character for the English at all and I couldn't have imagined that many people cared that much about Diana before.