Top Gear presenter Richard Hammond is making "very good progress" as he recovers from a crash in a jet-powered car on an airfield near York.
A spokesman said if Mr Hammond continued to do well he would eventually be transferred to a hospital closer to his home outside Cheltenham.
He has also received "hundreds" of cards and flowers, which have been placed in a separate room.
Donations to the air ambulance which flew him to hospital stand at £188,000.
The appeal to raise funds for Yorkshire Air Ambulance, which is supported by Mr Hammond's family.
A group of motoring enthusiasts has set up a web page for contributions on behalf of Mr Hammond, whose nickname is "Hamster".
Mr Hammond, 36, is receiving treatment for a brain injury on a general ward at Leeds General Infirmary following his crash during filming for the BBC show.
Among those who have donated is comedian Freddie Starr, whose agent said he gave an undisclosed sum to the Yorkshire Air Ambulance "for his own personal reasons".
The 62-year-old told the Sun newspaper: "I have a helicopter's pilot licence so it is something I feel very strongly about.
"These guys and girls do an amazing job and it costs a lot of money. Hopefully, my donation can help people in real danger like Richard."
All the money raised so far has "brought forward" plans to buy a new, second helicopter, Yorkshire Air Ambulance charity chief executive Martin Eede said.
"In over 25 years in the voluntary sector I have never known anything like this - we are completely overwhelmed, grateful, thankful," he told BBC News.
The BBC has said it has started an investigation into the accident, which happened at Elvington airfield while Mr Hammond was driving at speeds of up to 300mph.
It also confirmed the final part of the Best of Top Gear had been postponed indefinitely and the new series, due to begin on 8 October, would be delayed.
Mrs Hammond said the family had been overwhelmed by the flowers and messages of support received from well-wishers.
But she added: "However, Richard is now beginning to worry that [co-presenters] Jeremy [Clarkson] and James [May] will start taking the Mickey, so it would be great if - instead of flowers - people could make a donation to the Yorkshire Air Ambulance.
"The service is entirely funded by charitable donations and there is little doubt in my mind that without it, Richard would not be making the excellent progress he is."
Mr Hammond had been driving a jet-powered dragster similar to the Vampire used by Colin Fallows to set the British land speed record of 300.3 mph.
Mr Hammond, from Cheltenham, Gloucestershire, had to be cut free after the car "veered off to the right" and its parachutes opened during the drive.
Primetime Land Speed Engineering, which supplied the car and a support team for the event, said the vehicle "had been prepared and was being operated to the highest of standards".