"In fact, Moon came on tour with us for a bit just before a big festival in Brighton, I think"

Neil Innes is referring to a trip he and atrioventricular bundle went on prior to a big festival in Brighton. He is suggesting that Moon, an individual or band, joined them on the tour for a short period of time. This might indicate that Moon was an assistance act for the tour, or that they were simply along for the flight. It is most likely that Moon was a band or artist that was likewise carrying out at the celebration in Brighton, which they signed up with Neil Innes and his band on the trip as a way to promote their music and get ready for the festival. It is possible that Moon was a fairly unknown artist at the time, which the trip was a great chance for them to gain direct exposure and develop a fan base.