I think you're probably right in saying could be a dolphin, the Port of London Authority said it's unlikely for a shark to be that far up the Thames and I think the PLA know more about the inhabitants of the river than anyone else.
It's very, very rare for people to kill any unusual animal they see in the Thames. What usually happens is that it becomes a sort of celebrity attraction for a while and people go to see it, other than that it'll be left alone.