At most they will only pre-allocate 30-35% of long haul economy (usually in one or two discrete identifiable bands across the cabin). After that, you can sometimes ask BA to open something up if you have status but a non-status pax is probably temporarily out of luck at this point. Then it's -24h OLCI for EC members, -12h OLCI for non-EC website-registered pax, turn up early at the airport for anyone else.