Officers had begun a manhunt as they tried to trace a silver Ford Ka, which is believed to have been damaged in the crash in Willingale Road.
Debden Park is a mixed academy school for pupils aged 11 to 18, which specialises in the performing arts and received a rating of “outstanding” in its most recent Ofsted inspection, according to its prospectus.
A statement from Gascoyne said: “As a school and a community we are devastated to say that as a result of the incident in Willingale Road this afternoon, it is with great sadness that we must report that a 12-year-old student from our school has sadly died.
“Our thoughts are with the family and all those affected. As a school we continue to work with the police supporting the ongoing investigation.
“The school will be open tomorrow with a number of counsellors on hand to support our community.”