Two Met Police officers called to the Streatham attack are being investigated for alleged dangerous driving and misconduct over a car crash.
The officers were travelling in convoy to the scene on 2 February after Sudesh Amman, wearing a fake suicide vest, stabbed two people.
One officer was involved in a crash with two other cars which injured him and a member of the public.
The Met Police Federation described the move as “a complete joke”.
The Independent Office for Police Conduct (IOPC) said the officers were under investigation on suspicion of dangerous driving and gross misconduct.
It followed a referral from the Metropolitan Police on Friday which said one of the drivers was in an unmarked car while the other was in a marked armed vehicle.
An IOPC spokesman said: “A criminal investigation does not mean that criminal charges will necessarily follow.
“Misconduct notices do not imply guilt but are to inform the officer that their behaviour and conduct are under investigation and the level of severity.”
The two officers have been placed on restricted duties and are not allowed to drive police vehicles while the investigation is carried out.
Ken Marsh, the chairman of the Met Police Federation, which represents more than 30,000 officers in the force, said: “The public will be appalled when they hear that brave police officers responding to a terrorist attack can be treated in such a manner.
“What kind of message does this send? These officers and their colleagues put their lives on the line that day to protect the public.
“Now potentially their careers are on the line. It’s absurd. A complete joke.”