Footage captured by a member of the public shows the woman dancing in the road in Engineers Way at around 11.10pm on Thursday (April 17).
She narrowly avoids passing vehicles, but a car is then seen driving into her and carrying her 30 yards on the bonnet, before throwing her to the ground.
Emergency services were called after the incident, but the woman was no longer there when officers and paramedics arrived.
The car also did not stop at the scene.
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Investigating officers want to identify the woman in the footage so they can ask her about the incident, as well as to make sure she is okay and gets appropriate medical attention.
Engineers Way was busy at the time of the hit and run, according to the Met Police, with many people having just left a concert by the artist Alkaline.
Officers searched the area and arrested a 33-year-old woman on suspicion of dangerous driving and drink driving.
She has since been released on bail to a date in early June.
Anyone with information is asked to call police on 101 or message @MetCC on X, giving the reference 8317/17APR.
To remain anonymous contact the independent charity Crimestoppers on 0800 555 111.
