Have flown this route a few times - always the afternoon 747 flight from LHR and have been lucky to have the refurbished 86J aircraft each time.
I do know from keeping an eye on the route that it can be a right old mixture though.
Happened to notice that the morning 777 flight has been a 777-300 recently.
BrianWBrazil has the best advice - do a dummy booking if you know the dates involved (or ask on here if anyone can check expert flyer for you).