The incident happened on the London-bound carriageway between Cobham and Gravesend on March 23.
Officers and South East Coast Ambulance crews attended and found a man seriously injured.
He was taken to a London hospital where he remains in a serious but stable condition.
His next of kin have been informed.
Police are now appealing for witnesses who may have travelled in the area between midnight and 5am.
Investigators are also appealing to anyone who may have stopped at the scene and not yet spoken to officers to come forward.
Anyone with information is asked to call 01622 798538 and quote reference RY/MD/020/25.
