The television and radio presenter raised millions to build the National Spinal Injuries Centre (NSIC) at the Aylesbury hospital.
Sir Jimmy began fundraising for the unit in 1972 after joining as a volunteer porter in 1969.
General Manager David Griffiths said: "We understand he effectively raised well in excess of £40m [for the unit]".
The NSIC was founded in 1944 by neurologist Professor Sir Ludwig Guttmann to treat servicemen who had sustained spinal cord injuries in World War II.'Inspiring and uplifting'
"By 1979 the buildings were getting dilapidated and the ceilings were starting to cave in," explained Mr Griffiths.
"What Jimmy did was take up the cudgel and started raising money for us to reopen."Continue reading the main story
If we, as patients of the hospital, felt that something needed to be done we could always go to him and he would use his influence”End Quote Paul Smith Former patient Sir Jimmy's campaign raised £10m within three years and led to the creation of a purpose-built spinal cord injuries centre.
The new facilities opened in 1983, Sir Jimmy became its patron and continued to take an active interest.
"We were always delighted when he turned up," said Mr Griffiths.
"Every time he talked to a patient or a member of staff you could see them smile and light up. He had a canny knack of inspiring and uplifting everybody so he was a very, very valuable patron for us."
Paul Smith from Hertfordshire was a former patient and is now Executive Director at the Spinal Injuries Association.
"A great many spinal injury people really do owe him a debt because we don't know what the centre would have been like without all the input that he had," he said.
"He did have a lot of sway. If we, as patients of the hospital, felt that something needed to be done we could always go to him and he would use his influence."'Slightly surreal'
Mr Smith first met Sir Jimmy when he was in the unit following a motorbike accident 36 years ago.
"I was head to toe in plaster and it was slightly surreal [coming round and] looking down to the end of your bed and seeing Jimmy Savile standing there," he said.
"As a volunteer he was always around and about, it was great to see him there and to realise that life could be a bit of fun."
Mr Smith saw Sir Jimmy again at an outpatients appointment and it was this encounter which led to an appearance on his BBC TV show Jim'll Fix It.
"I was thinking about going back to work and he suggested I became a DJ as I was a bit of a mouthy individual," explained Mr Smith.
Sir Jimmy suggested he do hospital radio and write to Jim'll Fix It asking to host it.
"He gave me about three quarters of the show to host which stood me in good stead and I got all sorts of contracts and work out of that."
The hospital was still planning to hold a celebration on 31 October on what would have been Sir Jimmy's 85th birthday.
"A book has been put together from all the staff and patients for him as a birthday card," explained Mr Griffiths.
"Very sadly he is never going to see it but we're going to keep hold of it for anybody who wants to see it because I think it reflects what staff and patients actually thought of Sir Jimmy, he was very, very well-loved."