The construction will start on the rear of the Bloodhound vehicle in January, with an attempt on the World Land Speed record expected in 2012.
"We've got companies all over the world wanting to sponsor the car," director Richard Noble told BBC News.
"We've actually got more people who want to financially back this thing than we've got space for them," he added.
Noble also made an appeal to the public to help prepare the vehicle's racetrack. This is a dried-up lakebed in Northern Cape Province, South Africa, known as Hakskeen Pan.
Before the Bloodhound car can hurtle across this flat expanse of land, it must be cleared of all loose stones.
A rock thrown up at 1,000mph has the potential to do serious damage to the car's thin alloy bodywork and even cripple its four solid aluminium wheels.
With the assistance of the Northern Cape government, work has just started to prepare the track. A team of 300 local people has begun sweeping an area 20km x 1.5km, picking up any stones in their path.