Officers were called at 5.15pm on Sunday, June 29, to reports of two fires at Abbotswood Nature Reserve in Romsey.
Firefighters extinguished the blazes, and no injuries were reported.
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Police believe children were in the area at the time who many have been involved in the incident and are conducting inquiries.
They are now asking for anyone who may have witnessed suspicious activity to come forward.
Anyone with information that could assist the investigation is urged to contact 101, quoting reference number 44250287511.
