Koppel was born to Jewish parents in Berlin, where he grew up, but after the Nazi takeover of Germany, they emigrated to Prague, Czechoslovakia in 1933, where he began his education as an artist.
From 1944 onwards, Koppel lived in Dowlais, near Merthyr Tydfil, Wales, where he taught art to both children and adults, and the surrounding countryside was an important subject in his paintings, showing mystical influences and often bordering on the fantastic.
The decaying industrial areas of Wales were also present in his work, whilst his murdered mother is a motif in a series of papers.
In early 1949 he married fellow artist Renate Fischl a German exile born in Dresden, herself a painter of some repute and student of the East Anglian School of Painting and Drawing.
Finally, in 1974, he settled down in Cwmerfyn, near Aberystwyth, remaining active as an artist, and in his later work he experimented with various materials such as fibreglass and resin.