The BBC could face unlimited fines if found guilty of health and safety breaches.
A full investigation into the crash was launched today by the Health and Safety Executive, which sent an inspector to the site. It will gather evidence which could lead to a prosecution of the BBC.
An HSE spokesman said today: "The competence of Hammond to handle cars at that speed would be something both us and the police would look at.
"The competence of the driver should have been taken into account in the BBC's risk assessment. I presume the inspector will want to see that."
Richard Noble, a former holder of the world land speed record, today welcomed the inquiry.
He said: "I am all for this. There will be a report published on this and everybody will learn from it."
North Yorkshire Police said its collision investigation unit was examining the wreckage for clues.
At this stage there was no evidence of any criminal wrongdoing such as the car having been tampered with. A spokesman said: "Very few people have experience of driving jet cars. I don't know what his (Hammond's) experience is."
The investigation will be assisted by Colin Fallows, holder of the British land speed record, and Mark Newby, who were supervising the runs. They owned and built the Vampire.
A spokesman for the two men said today: "They have no idea what went wrong. They are very upset for Richard. They will remain at the site for a couple of days.
"The Vampire has been driven hundreds of times by professional drivers at these very high speeds. Safety is absolutely paramount. Other journalists have also driven the car previously at that speed."
Mr Noble, who topped 633mph when he broke the record in the US in 1983, raised a series of concerns. He questioned whether Hammond was sufficiently experienced to be driving a jet car at such high speeds.
"I suspect there were very substantial media pressures there. The thing was seen as a television event. And maybe the guys (at the BBC) didn't understand the risk they were running," said Mr Noble.
"It is very easy to be carried away and not realise the enormous risk you are actually taking. It is particularly dangerous on a very short runway."
Mr Noble said the airfield in Yorkshire, at 1.9miles, was short compared with the 11 miles of Bonneville salt flats in Utah and the 13-mile runway at Black Rock desert in Nevada where he broke his record.
He added: "A jet car has virtually unlimited power. If the car comes unstuck at any time and the wheels leave the ground it keeps on going because it effectively becomes a firework. The driver has to be highly experienced."
The BBC today confirmed it has launched an internal investigation.
A spokeswoman said: "The circumstances will be fully investigated by the BBC and this process began last night."
She refused to comment any further on what risk assessments, if any, the Top Gear production team carried out before the stunt, saying: "Until the BBC's investigation is complete it would be inappropriate to comment on the details of what happened."