The force said the man is described as “white, aged approximately 50 years old, around 5ft 6ins tall with grey hair” and that he was wearing “a red waistcoat or vest over a shirt and light-coloured trousers”.
The woman who witnessed the man expose himself lodged a complaint with the Met after attempting to report the incident to officers at the scene of the vigil.
A spokeswoman for the Metropolitan Police said: “The woman attempted to report the incident to officers who were at Clapham Common as part of the policing operation for the vigil.
“A complaint was received by the Met’s Directorate of Professional Standards. This was resolved to the satisfaction of the complainant.”
Crowds gathered on Clapham Common last weekend to join a vigil in remembrance of 33-year-old marketing executive Ms Everard, whose death triggered an outpouring of grief and anger at violence against women.
Detective Constable Luke Flood, from the Met’s Central South Command Unit, which polices Lambeth in south London, said: “I am appealing to anyone who was in the area and can help identify the man involved to contact police.
“Clapham Common was extremely busy on Saturday evening with people who had attended the vigil – many people would have been filming or taking pictures.
“I would ask anyone to check any material they captured and see if they can identify the man described.
“We also cannot discount that there may have been other instances of this nature in and around the Clapham Common area so I would urge anyone who has witnessed get in contact.
“An incident of indecent exposure can be an extremely distressing offence for those who witness it and it is one police take very seriously.
“Officers have spoken to the woman to offer her support and ensure she is kept updated with the progress of the investigation.”
Anyone who may be able to help police is asked to contact 101 or tweet @MetCC and quote CAD2602/18Mar.
Alternatively, they can contact the independent charity Crimestoppers anonymously on 0800 555 111.