Originally Posted by corporate-wage-slave

You did the right thing in terms of contacting BA as soon as you could and speaking to someone. Yes, they will give you an email address for the clinical letter, and they should be able to sort out the flight within a few hours. So if you get this arranged on Monday you should be good for Tuesday. The fare difference, no change fee, arrangement is correct (if you were airside then that would not apply! It's a free transfer if LHR / ARC handle it). I hope your daughter makes a swift and full recovery.