Parents in Bromley, south-east London are on alert as it has emerged that four attempts to snatch children have been made in a week.
The Metropolitan Police said that two boys were approached separately by a man in the borough on April 30 between 4pm and 4.30pm.
One of the boys, aged 11, was asked if he wanted a lift by a man in a black van on Whitmore Road in Beckenham, while an eight-year-old was approached in the nearby wooded area of Kelsey Park.
The Met received another report on Thursday of a male school pupil being followed by a man along a street on the previous day.
Despite what the police called a "lack of similarities" with the incident indicating it was not linked with the first two reports, the force urged parents to “remain vigilant”.
Earlier in the week, one parent tweeted to say: “Two hooded men on foot and another in a car attempted to abduct my son on his way home from school.
"They chased him into the park [Croydon Road Recreation Ground] but he ran into the basketball courts for two older teenagers for help, the men then disappeared."
"Our son maybe shaken up but he is safe at home with us," she added. "I don't want any parent to be posting about their missing child in the coming days/weeks/months! So I'm raising the alarm."
It led to Jane Holland, the headteacher of Clare House Primary School writing a letter to parents to warn them about the latest report, as well as addressing students in an assembly.
The latest incident involved the "perceived" attempted abduction of a young girl at The Glade shopping centre on Friday.
Two males were said to have been walking behind the girl in the south-east London borough when one attempted to grab her hand as it was raised in the air, before walking off.
The Met said the incident is not believed to be linked to any of the others. Superintendent Andy Brittain, of the Met's South Area Command said: “When we are made aware of potential incidents of this kind, we investigate them thoroughly.
“I am aware of varying reports online both in the news and on social media and I fully understand the concerns of parents in light of these reports.
“I would encourage the public to remain vigilant, but not to be unduly alarmed. Child kidnappings or abductions are, thankfully, incredibly rare, but we are not complacent.
"In order to provide reassurance to the community we have heightened our visible presence in areas where youngsters may gather and I urge anyone who feels worried or concerned to approach my officers.
“In addition, please be assured that if we have reason to believe that there is a specific danger we will make sure that our communities are fully aware immediately.
“I would strongly encourage members of the public to approach our officers if they have any concerns or have any information that could prove to be beneficial to our investigations.”
None of the children were abducted or harmed in any of the four reported incidents, the Met said.