Injured Stirling Moss thanks fans
The 80-year-old, who won 16 Grand Prix races between 1951 and 1961, called the accident a "shunt" and said he would be "bouncing back" soon.
Sir Stirling is recovering in hospital following the accident at his home in Mayfair, west London, on 7 March.
He said: "I would like to thank everybody kind enough to write to me."
'Take it easy'
Sir Stirling continued: "I am not feeling great, but I am feeling better.
"Obviously I am going to take it easy, which is a bit of a bore.
"But I should be bouncing back as soon as I possibly can.
"Hopefully that means I will be meeting a lot of you in the next few months."
The retired sportsman, considered by many to be the greatest Formula One driver never to have won a championship, also broke four bones in his foot and chipped four vertebrae when the lift door opened at the wrong time and he stepped into the empty shaft.