Shortly after 11pm on Friday 1 December police received multiple reports of people fighting on the Golden Jubilee Bridge and by the Royal Festival Hall on the South Bank.
"Enquiries were carried out that night and the Met quickly became aware of information suggesting that off-duty police officers were involved in the fight," said a police spokesperson.
Detective Inspector Nicholas Goldwater said: “Our CID team is working alongside colleagues from the Directorate of Professional Standards to ascertain the facts of the incident, which led to numerous calls being made to the police that night.
“We are pursuing all lines of enquiry to establish what happened, including viewing a large amount of CCTV footage. These CCTV enquiries are lengthy and ongoing.
“We would like to hear from anyone who was involved – including a group of men we believe to be of Romanian heritage – who may have information about the incident.”
The Met says that four officers have been placed on restricted duties while the investigation takes place. No arrests have been made.
A voluntary referral has been made to the Independent Office for Police Conduct.
Anyone with information or footage - or anyone who witnessed the fights but has yet to speak to police - is asked to call 101 quoting CAD 7908/01Dec.