Terry Glover, 51, is being sought by police over the crash, which also left five people injured.
Chief Superintendent Tracey Harman told reporters that police are working to establish if it was connected to an earlier incident.
Officers were called just after 3.20pm to reports a number of pedestrians had been involved in the collision in Loughton.
Police launched a murder investigation as they mounted a manhunt for the driver, who failed to stop at the scene.
Five people were hurt but none of the injuries are believed to be life-changing or life-threatening.
Those injured were two 15-year-old boys, a 13-year-old boy, a 16-year-old girl and a 53-year-old woman.
Police believe all the teenagers are pupils at Debden Park High School on Willingale Road.
East of England Ambulance Service mobilised 15 ambulances and 10 other vehicles, while three air ambulances were also sent.
Officers are still trying to trace the vehicle, a silver Ford KA with the registration number LS08 OKW.
Armed officers could be seen outside an address in Loughton.
Detective Chief Inspector Rob Kirby of the Kent and Essex serious crime directorate said: “This has been a truly shocking incident and my deepest sympathies are with all those involved.
“I would like to thank the many members of the public who have called us with information and spoken to our officers, as well as those who provided crucial medical assistance at the scene.”
Helen Gascoyne, head of Debden Park High School, said in a statement: “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.”
Tony Dibbins, a DJ for Absolute Radio 70s, said his daughter goes to the school.
He wrote on Facebook: “Feeling incredibly sad and angry this evening. Today a lad lost his life walking out of the school my daughter attends.”
He added: “This evening, I am thankful my princess is safe – However my heart is breaking for the parents who have not been so fortunate.”
Father Sam Stuart held a mass at St John’s Church in Loughton following the collision.
He wrote on Twitter: “Church will be open tomorrow for prayer, lighting candles and if anyone needs to talk.”
Anyone with information or dash cam footage are urged to call police on 101 quoting incident number 726 on 2 December. Or they can call Crimestoppers anonymously on 0800 555 111.