I had this same issue when my team was in European football. I didn't have quite the extent of flight bookings the OP is considering, but I did have multiple hotel bookings well in advance (free cancellation) and also 3 flights booked the day of the draw with 2 pax on each. I then phoned and cancelled 2 of them once the draw was made.

I had no issue with cancelling the 2 flights but I was more worried that BA's systems might flag that I was booked on multiple flights at around the same time and see it as a fraud issue or something - but no problems in the end.