May clearly did not want to speak with Brundle and palmed the broadcaster away, before Brundle went in again to try and speak with the musical icon.
The legendary guitarist claimed he didn't know anything about F1, before an awkward silence between the pair occurred.
The incident has led to many fans on social media responding badly towards May, with Brundle well-revered in F1 circles.
However, the former F1 driver believes he was in the wrong, taking to X to stick up for the musician.
"It is me who should be apologising to Sir Brian May, not him to me for the gridwalk on Sunday at Silverstone," Brundle said.
"I didn’t address him as Sir Brian, and I shouldn’t have approached him twice when he wasn’t up for a chat on live TV. Nobody is ever obliged to talk to me on the grid, or anywhere else for that matter."
It is me who should be apologising to Sir Brian May, not him to me for the gridwalk on Sunday at Silverstone. I didn’t address him as Sir Brian, and I shouldn’t have approached him twice when he wasn’t up for a chat on live TV. Nobody is ever obliged to talk to me on the grid, or…