As for winning the Grand Chess Tour, Giri is the favorite. The standings for the relevant players:
Giri - 13 Grand Chess Tour Points
MVL - 12 Grand Chess Tour Points
Aronian - 15 Grand Chess Tour Points
Carlsen - 14 Grand Chess Tour Points
Grischuk - 8 Grand Chess Tour Points
The winner of the London Classic gets 12 points if 1st place is shared and 13 points if it is not shared. Then 2nd place is 10 points, and 3rd place is 8. There is tiebreak procedure, but the website says that it can't be calculated until the end of the tournament.
Grischuk doesn't seem to have any chance, but Carlsen or Aronian could still win the Tour if they win their last games while Giri and MVL draw. As the forecast below indicates, there is a substantial probability of this happening.
But perhaps the biggest winner of the London Chess Classic is...Vladimir Kramnik. He's not even playing, but he has benefited from the tournament. Both Anand and Topalov have dropped enough points that now the Russian is in 2nd place in the live ratings. I don't recall Kramnik playing in many top tournaments this year, but when he has played, he has done well. His rating has climbed to 2796.