The first name "Soft" obviously references the past band Soft Machine while the second name "Heap" comes from the initial letters of the band's founders' first name: Hugh Hopper (bass), Elton Dean (saxophone), Alan Gowen (keyboards) and Pip Pyle (drums).
[1] The live album Rogue Element was recorded on that tour in May 1978 at Chez Jacky "A L'Ouest de la Grosne" Bresse-sur-Grosne, France and was released in 1978.
John Greaves (also from National Health) replaced Hugh Hopper on bass in 1979–80, and after Alan Gowen's death in 1981, Mark Hewins joined on guitar, the new 1981 line-up becoming: John Greaves, Elton Dean, Pip Pyle and Mark Hewins.
The new line-up toured intermittently throughout the 1980s, occasionally including guests such as Fred Frith and Phil Minton.
No records were released during the 1980s although the band kept gigging, embarking on four tours during the decade with a total of 25 European concerts, culminating with a gig in a circus tent (built especially for the band) on 11 May 1988[1] at the Festival "Jazz sous les pommiers"[1] in Coutances, France that was recorded and broadcast live by FR1 Radio (according to Mark Hewins).