The man, who sometimes wears women’s clothing, has been targeting victims since 2019, police said on Wednesday.
Most of the 12 reported incidents took place in the Kentish Town area.
He is described as white with olive skin, between 5ft 6 and 5ft 8ins tall and of a large build.
He has dark receding hair and facial stubble and speaks with a European accent.
On several occasions he has worn a hat and women’s clothing, police said.
The Met urged other potential victims to come forward.
A spokesman said: “Detectives are keen to hear from anyone who has information concerning the identity of this male or from any women who believe they have been approached by him but have not yet spoken with police.”
Anyone with information can contact police on 101 or Tweet @MetCC quoting 3773/7SEP21
