Sutton police want the public's help after a man was spotted on several occasions outside Wallington Girls' School.
Police believe he made a number of inappropriate approaches to girls aged 12 to 15 before and after school on Thursday and Friday last week.
The man is white, aged in his late teens or early 20s, with a chubby build, round face and blond hair.
He was seen wearing black tracksuit bottoms and white trainers.
Detective Constable Tim Budd has asked children and local residents to remain vigilant in the area around the school in Woodcote Road, Wallington.
He said: "It's important that we identify and speak to this suspect."
To report any information contact DC Budd at Sutton police station on 020 8649 0744.
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