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.

Mohanna Abdhou, 20, was shot in Malvern Road, Kilburn, and died at the scene.
Ms Abdhou, known as Montana, was approached by "two males" on bicycles who fired "shots at her group of friends".
Police said nothing in her background gave "any suggestion she would have been a target" in the shooting, which took place on Friday, 26 May.
CCTV images of the men believed to have carried out the shooting have also been released.
Footage shows the two suspects at 20.53 BST cycling along Malvern Place, seconds before turning into Malvern Road where the shooting took place, police said.
They are described as being of slim to medium build, both wearing dark clothing and concealing their appearance through the use of face coverings.
A 21-year-old man who was arrested at the scene on the night of the attack has been released under investigation pending further enquiries.
A 19-year-old man and a man, aged 20, were arrested in west London on suspicion of murder in the early hours of 31 May. They have been bailed pending further enquiries.
Ch Insp Andy Partridge said: "Valuable information has been passed to us but we are certain that people in the local community know who has committed this horrific attack.
"These individuals should not be shielded by friends or family, or supported in any way.
"No right-minded person would want those responsible for depriving Mohanna's family from ever seeing her again, to evade capture.
"Mohanna's family deserve answers and that will only happen if the local community tells us who carried out this attack."
A team of schoolchildren's rocket-powered model car has broken the world speed record, it is claimed.
[NEXT_CONCEPT]
A £10,000 reward has been offered following the murder of a woman shot dead by two men on bicycles in London.