I have usually always known when my travel dates / times would be and on the occasions that there might be last minute changes, my company has paid for a flexible fare. Normally, I have made the original flight.

I have a trip lined up whereby I won't even know what day I am flying on, let alone the time; my company will be purchasing a fully flexible fare for me, for a random time / date (educated guess as to when I might need it).

Has anyone had an experience of this sort of thing?
Do I call up BA as soon as I know the time/date I need to travel (I know that it will be very short notice)?
Do I just turn up at LHR and try to get on the next flight?

Just as a point, the flight in question will be LHR - BRU, so plenty of flights per day.