"When we actually recorded it for real, George loved it and told me he loved the changes I had made. The thing was, I hadn't changed a thing, " said Goodwin.
Having cleared that early hurdle, The Trap has certainly lasted the distance.
"I'm not really sure how it became the BBC's marathon music, but I'm pleased that it has, " said Goodwin.
"I never intended it to accompany running, but it was supposed to depict a certain amount of energy being expended.
"Having said that, I had no idea the BBC had started to use it.
"The first I knew of it was when my wife shouted to me while I was in the shower one morning, 'They're playing your music during the marathon!'."
It was with Reed in mind that Goodwin penned his tuneAlthough The Trap is Goodwin's only sporting theme tune, he has written over 60 film scores, including the music for hits such as Where Eagles Dare, Monte Carlo or Bust and Those Magnificent Men in their Flying Machines.
Now living in Brimpton Common, near Reading, Goodwin still travels the world playing his music with leading orchestras.
But for the five million viewers who watch the BBC's race coverage, Goodwin will always be best known for the London Marathon 'theme tune'.
"Yes, it's funny, " said Goodwin. "Oliver Reed liked it a lot too.
"We tried to get Ollie to record a version of him singing a few words that somebody wrote to accompany the tune.
"He did a reasonable job at dinner one evening, but when we got to the studio his voice wasn't really up to it.
"And I remember him turning around to us and saying, 'If you wanted a singer you should have hired Frank Sinatra'."