Without wanting to be too gruesome, the likes of the eyes, lips and other soft tissues usually get eaten quite quickly by various animals, birds and marine life.They were talking about identifying him by his teeth, DNA, etc.
Which leads me to believe that maybe he was being eaten? Or maybe just the erosive power of the water was capable of doing sufficient damage in that relatively short period to make visual id problematic.
I have no idea what's in the Thames but I'm going to guess it's piranhas.
There are reasons for the old jokes, memes and pictures about things like crabs in eye sockets, or ravens/crows landing on the head of a dead soldier.
Basically there is a good chance there wasn't much of his face left, on either side.