The guitarist, who has changed his name to Pearl Thompson and turned his back on music to dedicate his life to painting, was stunned when Plant, a fan of The Cure, invited him to hit the road with him and Page on the back of their hit No Quarter album two decades ago.
He recalls, "I'd left The Cure to pursue my painting and then suddenly, out of the blue, I got a call from Robert Plant, which I thought was a hoax. He was really into The Cure, which I thought was interesting, and they invited me up to see if we all got along.
"It was an opportunity I couldn't really turn down. We did a Tv show together but it went so well that they just started talking about going out on a tour and they asked me if I wanted to do it with them. It was very freeing as I was really there just as a guitarist. But it was pretty daunting playing alongside Jimmy Page, especially when you consider that quite often there would be a change of set list and they'd throw in a song that nobody had rehearsed, which would be used the next night, so you'd have to go back and do your homework in you hotel room and then turn up and just play things like The Song Remains the Same.
"It was very difficult but challenging and exciting."
And Thompson insists there was no sign that Plant and Page were anything but great friends: "There wasn't any drama. It was a big set up. There were two orchestras and rehearsals were interesting."
Plant and Page have since fallen out over the singer's reluctance to reactivate Led Zeppelin after a one-off reunion in 2007.