Pupils at The Joseph Whitaker School in Rainworth, Nottinghamshire, broke the record at their first attempt with a speed of 478.1mph (769.4km/h).
However, later, a different car they had built went even faster and hit an average speed of 533.1mph (857.9km/h).
The footage from the Rolls-Royce runway in Hucknall will now be sent to Guinness for verification.
If the speed is verified, it will have smashed the existing record held by Samvir Thandi  and the Heathland School in Middlesex, whose car reached 287.6mph (462.84 km/h) in March.
The Young Engineers tweeted: "We have a confirmed 478.1mph average by Red Shift! Well done to all the young engineers - world record holders!!"
However, after a further attempt with a car they had nicknamed Insanity, the team went on to set an even bigger record.
Phil Worsley, the teacher in charge of the Young Engineers club, said: "When people watch our rockets they don't anticipate the speed, their heads lag behind the car.
"[The pupils] are absolutely amazing. The most amazing bunch of people I've ever worked with."
The cars, which are about 45cm (17in) long and constructed from carbon fibre, run on titanium wheels and are guided by a 250m (820ft) steel cable.
All parts have been stuck together with strong glue and at the end of each run, the cars come to a stop using small parachutes.
The pupils have been working on the project for about a year.
A team of schoolchildren's rocket-powered model car has broken the world speed record, it is claimed.