Police are are looking into seven reports of men approaching children in Dartford and Gravesend.
The reported incidents date from Friday, February 10 to Wednesday.
Schools across both boroughs have sent text messages to parents to alert them of potential dangers.
More top news
Philippa has the weather update for the east
Philippa has the weather update for the west
69 year-old Peter Sutcliffe has been photographed in The Sun on Sunday on a visit to Frimley Park Hospital in Surrey.