Having walked only a couple of hundred yards from the shop, they crossed near the Makkah Masjid Mosque.
The road is used by local drivers as a short cut, but has speed bumps, Mr Taylor said.
Detectives know the car is a mark four model, meaning it was made between 1998 and 2005.
"We know the vehicle slowed down and we know they have then sped off," he said.
"I would appeal to that driver to come forward so he or she can tell us what happened."
CCTV footage of the incident has already been examined and experts will study more footage in a bid to identify the car's registration number.
"This is a small, close-knit community and people want to help," the detective said.
Sabam's father thinks she is "the apple of his eye", Mr Taylor said, while her brother Raham, who was due to start nursery in October, is described as being full of energy.
The children went on the errand with a cousin who escaped injury.
The Eid celebrations mark the end of Ramadan, the holy month of fasting observed by Muslims.