Emaan Shah was due to leave the country on the evening of June 10 at the end of the holiday with her family.
But in the afternoon she became separated from her mother whilst they were shopping on Oxford Street, one of the city's busiest shopping districts, and has not been seen since.
"The disappearance is out of character and officers are keen to trace her as soon as possible," the Metropolitan police said in its appeal.
"Emaan is described as 5 feet, 3 inches tall, of slim build with brown wavy hair. When last seen she was wearing a black jacket with a Manchester United logo on the chest, grey trousers and black and white trainers," the appeal adds.
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She was carrying some cash with her but did not have a mobile phone on her.
Her father, Tanvir Shah, who runs an advertising company in India, said, "We are frantic with worry. There is no reason why she should go missing. She was happy and had just done well in her exams and was looking forward to choosing a university."
The Met police is now trawling through CCTV recordings of the area and have urged anyone with information to call 101.