The 63-year-old radio DJ has just quit the corporation after 40 years and he and Mark Kermode have signed a deal with Sony to launch their new movie review podcast Kermode & Mayo's Take.
Mayo told the Radio Times: "When Sony come along and say, ‘We will invest in this programme in a way that it hasn’t been invested in so far’ you think, that’s interesting."
Asked to elaborate on examples of being frustrated by the BBC red tape, Mayo cited a contest he ran on his Five Live show.
"For instance, we did a very successful short-film competition called Well Done U. The quality of the entries was brilliant, but there are so many BBC hoops to jump through to actually get something like that on the air that after a while people stop trying, because it’s soul destroying. This way we’ll be able to bring things like that back.”
The former Radio 1 Breakfast Show and Radio 2 Drive Time presenter has said he and film critic Kermode, 58, would struggle to gain support to launch their own film show at the BBC now, with "two middle-aged men" presenting it.
He said: "The truth of the matter is, if you were going to start a new film show on the BBC right now there would be no chance of me and Mark being asked to do it."
Mayo joined the BBC in 1982. He hosted the Radio 1 Breakfast Show for five years in the 90s and Radio 2's Drive Time slot for nine years between January 2010 and December 2018.
He and Kermode co-hosted their own film review show on BBC 5 Live for 21 years, before it came to an end on 1 April this year.
Within minutes of their final show airing on BBC radio they announced their new movie podcast Kermode & Mayo's Take.
Mayo told Kate Thornton on White Wine Question Time: "Leaving Radio 1 and going to 5 Live that was the was the most disruptive, and the most challenging, and then ultimately, the most rewarding [new start].
"Being at Radio 1 was everything I'd wanted to be. I just wanted to be a Radio 1 presenter, and then when I was one, I wanted to be the breakfast show presenter, and then I was the breakfast show presenter.
"But everything has its course, everything has its lifespan."
Watch: Simon Mayo discusses being on air live during the 9/11 attacks