The incident happened in Court Road near Old Priory Avenue just after 4.30pm today (January 7).
Officers and London Ambulance Service crews attended and treated a 30-year-old man for a neck injury.
He was taken to hospital where his injuries have been assessed as non-life-threatening or life changing.
A 40-year-old woman in one of the vehicles involved was not injured, but was taken to hospital as a precaution.
Nobody else was injured in the incident and no arrests have been made.
A spokesperson for the Metropolitan Police said: “Anyone with information that could assist police is asked to call 101 quoting CAD4729/07JAN26.
“Alternatively, call the independent charity Crimestoppers anonymously on 0800 555 111.”
