The vandalism is believed to have taken place at around 4am on Saturday July 3 and the messages were etched onto the side of a vaccination tent in Greens Lane.
Officers have called on the public to help them identify a woman who they believe could assist with their enquiries.
Accompanying the appeal, police have released an image of a woman wearing a yellow outfit.
PC Sunny Parbat, from the Metropolitan Police, said: “As well as being distressing to those who had to see the messages, it is also disheartening that at a time when we should all be united as a nation in the fight against this deadly virus, some individuals think this kind of behaviour is acceptable.”
Anyone with information which could assist the investigation is asked to call 101 quoting ref 28748/04JUL21 or email email@example.com.