The incident prompted Malmesbury primary school to issue a warning to parents about collecting their children from school yesterday.
A police statement said: “We received a report yesterday (22/01/19) that at approximately 1pm a 10-year-old child had been followed by a van driver in Gloucester Road.
"The man is described as white, aged in his 40s, with short brown hair and a beard. He was wearing dark clothes and is believed to have been driving a Vauxhall panel van.
"The child was not grabbed or injured during the incident. We increased patrols in the area yesterday afternoon and would urge anyone who sees anything suspicious to call police on 101.”