He was one of the most important blues musicians in Denmark, and he was known outside his own country, when in the late 1960s he met Alexis Korner and the two formed the bands New Church, The Beefeaters, CCS, and later Snape.

They formed New Church, and then in 1970 CCS around Korner and Thorup, the rest of the line-up was rather loose and depended on the availability in the schedules of many musicians.

They had several hit singles, commencing with a cover of Led Zeppelin's "Whole Lotta Love", which was used as the theme for BBC Television's Top Of The Pops.

King Crimson members Boz Burrell, Mel Collins, and Ian Wallace left Robert Fripp [clarification needed] in New Orleans to continue on tour with Korner.

Thorup mostly played rock or blues, but he also got a local pop hit, recording a Danish version of Kenny Rogers and Dolly Parton's "Islands in the Stream" with Anne Grete in 1984.