Emergency services were called to the first incident at 3.40am on Saturday and to the second just after 1.30am on Sunday.
A 23-year-old man injured on Saturday and a 43-year-old man who suffered stab injuries on Sunday were both treated in hospital, the Metropolitan Police said.
The force said the assaults are connected and have released a CCTV image of a man they want to question as part of their investigation. No arrests have been made.
“There is absolutely no place for violence on the rail network, and detectives are working at pace to investigate these two connected incidents,” Detective Chief Inspector Gareth Davies said.
“Passengers will see an increased police presence at the station while officers carry out their inquiries.
“We are urging anyone who was in the area at the time