May, who has just recovered from a hamstring injury, covered 10.49 metres per second in a personal best 40-metre dash as he tested his fitness ahead of the second instalment of the autumn series against the Wallabies at Twickenham.
Had May maintained his speed over 100 metres he would have eclipsed Bolt's record of 9.58 seconds by five hundredths of a second.
"I was gobsmacked that I did it really because I had just tweaked my hammy the week before," he said.
"It was a 40 or 50 metre sprint. It was a rehab run. I was shocked. I didn't think I would go anywhere that fast. I knew I had to run flat out to test the hamstring.
"I was pretty nervous about doing it but it was fine. And I ran quick as well and it was a bonus.
"We have spoken about Australia's kicking game and we want to put pressure on that and hopefully get some good opportunity to run the ball back at them."
The Leicester wing forms a rapid back three alongside Anthony Watson and Elliot Daly - possibly the fastest trio fielded by England - and they have been given the license to counter attack by Eddie Jones.
England are chasing a second win of the autumn Test series after an unconvincing victory over Argentina last weekend.