The disorder broke out shortly after 11pm with groups of people fighting on central London’s Jubilee Bridge and by the Royal Festival Hall.
In a statement on Friday, Scotland Yard said it became “quickly” aware of suggestions that off-duty police officers were involved in the fracas.
Four officers have been removed from public-facing duties while an investigation takes place. No arrests have been made.
The officers from the Met’s Territorial Support Group and Taskforce public order units were on a pre-Christmas night out.
In October, two of their TSG colleagues were dismissed over the “highly distressing” stop-and-search of black athletes Bianca Williams and her partner Ricardo Dos Santos in July 2020.
Met Detective Inspector Nicholas Goldwater said in a statement: “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 said it had voluntarily referred itself to the police watchdog, the Independent Office for Police Conduct (IOPC), and that it was awaiting guidance on whether it would investigate independently or refer the incident back to the Met.
An IOPC spokesman said: "“We were notified by the Met about this incident on Monday. We’ve asked for more information so we can assess what further action may be required from us."
Officers investigating the disorder ask anyone with information or footage, or anyone who witnessed the fights but has yet to speak with police is asked to call 101 or ‘X’ @MetCC ref CAD 7908/01Dec.
You can also provide information anonymously to the independent charity Crimestoppers on 0800 555 111.