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The 36-year-old was taken by air ambulance to Leeds General Infirmary's neurological unit on Wednesday.
A hospital spokesman said: "He has seen some improvement overnight, but remains in a serious but stable condition."
Mr Hammond had been in a dragster-style car capable of reaching speeds of about 300mph at Elvington airfield near York.
The hospital said his wife was at his bedside and, at the request of his family, no more information would be released.
The crash will be investigated by the Health and Safety Executive and the BBC.
The BBC said in a statement: "We are looking into all the factors of this accident and it would be inappropriate to comment further at this stage until we know the full situation."
The dragster car he was driving was believed to have been travelling at about 300mph when it crashed.
Motoring expert Adam Rayner, of Fast Car magazine, said that at those speeds the driver would experience forces similar to those endured by fighter pilots.
"These cars accelerate at 6G - the force is breathtaking and stopping is a real difficulty," he said.
Former firefighter Dave Ogden, who runs private firm Event Fire Services, was one of the first people at the scene of the crash.
He said: "We were down there with Top Gear who were filming him trying to break the British land speed record.
"On the previous run, the car had just gone over 300mph but I am not sure if it had broken the record.
"They had just done one more run and were planning to finish when it veered off to the right.
"One of the parachutes had deployed but it went on to the grass and spun over and over before coming to a rest about 100 yards from us."
He said his crew and an ambulance that was already on the airfield rushed over and found the car upside down and "dug in" to the grass.
Mr Ogden said he felt for a pulse and heard Mr Hammond breathing before the emergency crews worked together to turn the car the right way up and then cut him free.
He added: "He was regaining consciousness at that point and said he had some lower back pain. But he was drifting in and out of consciousness a little bit."
He was initially reported to have suffered serious head injuries and was taken to the neurological unit of hospital by helicopter.
Former Top Gear presenter Quentin Willson said the presenter was "irreplaceable".
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I hope it's not a spinal inury, but I wouldn't be suprised.
Simon
i hope he gets better top gear is my best tv show 
He's also talking so hopefully he will make a full recovery. 
