Eddie Harvey: Expressive trombonist who became one of the finest teachers of jazz

'Show us your balls, pal!' was Woody Herman's cry to any player who he felt was underperforming

Three of the Johnny Dankworth Seven in 1951: from left, Dankworth, Harvey and Don Rendell (Jazz Index)

As well as distinguishing himself as one of the most accomplished arrangers in British jazz, Eddie Harvey became an outstanding teacher of the music that he loved. He devoted most of his later years to spreading his knowledge, whether it was to individual students, at music colleges, collectively to the youngsters in his big bands, or to jazz appreciation courses that he organised in his retirement. He amassed a huge range of qualifications and, with his amiable outlook on life, was an ideal teacher – no one would argue that he was the best in the jazz field.

He was also an expressive trombone soloist or section player and, in the Humphrey Lyttelton band, switched between piano and trombone. "Show us your balls, pal!" Harvey liked to tell the story of his experience working for Woody Herman. If Herman called you "pal" it meant you were in trouble. Harvey played trombone in Herman's Anglo-American Herd that toured Britain in 1959. It included a sprinkling of American musicians like Bill Harris, the trombonist who had been Harvey's and every other trombone player's hero since the 1940s.

At its first rehearsal the Anglo-American Herd sounded insipid and awful. Herman and his Americans overawed the British musicians and there was no team spirit in the band. After one of the British saxophone players had played a particularly limpid solo Herman stood before him and put his face close to the man's.

"Show us your balls, pal!" roared Herman. The shock wave hit the whole band and it was instantly galvanised. Within an hour it had become one of the most exciting big bands ever put together in this country. No one enjoyed the tour more than Harvey, who throughout it sat in the next chair to Bill Harris. He admired Harris's Conn trombone and Harris arranged to get him one. "Unfortunately I had no money at the time," said Harvey, "so he had to send it back." The two became close friends and stayed in touch until Harris's death in 1973.

Harvey's playing pleased innumerable American stars, not least cornettist Rex Stewart and trumpeter Buck Clayton. Between them Clayton and Harvey wrote the repertoire for the successful tours with Humphrey Lyttelton's band in the late 1950s.

Harvey had begun to learn to play classical piano when he was seven, and took up the trombone as a teenager when his family had moved south from Blackpool to live first in Gosport and then Sidcup during the 1930s. His first job was in an accordion band in Kent, where he played alongside his lifelong friend, the clarinettist Wally Fawkes.

Harvey was a founder member of George Webb's Dixielanders, generally regarded as the band that started the "revival" movement (of New Orleans jazz) in Britain in 1943. Such was the purity of ideal that the band members held a kangaroo court to try Harvey when they suspected him of having "dance band" leanings. He left the Webb band for National Service in the RAF in 1946.

By the time Harvey joined trumpeter Freddy Randall's band in 1948 he was a sophisticated and eloquent trombone soloist. It was while with Randall that he first began writing arrangements. Leaving after more than a year, he worked for Carlo Krahmer, Graeme Bell and Joe Daniels. He then became the first traditional musician to escape into modern jazz when he played briefly for Vic Lewis and then, in March 1950, joined the Johnny Dankworth Seven. At this time he also studied at the Guildhall School of Music for two years. He stayed with Dankworth, by now leading a big band, until January 1955, when he left to become a freelance arranger and instrumentalist.

Throughout the late 1950s Harvey worked with bands led by tenor saxophonist Don Rendell. He appeared with Phil Seamen's band in the film The Golden Disc: The In Between Age (1958). He began writing for television, ran his own occasional big band and played on the Top Brass tour of Britain with Clark Terry, Bob Brookmeyer and Maynard Ferguson in 1966. He was also in small groups that shared the bill on tours by the Gerry Mulligan Quartet and the Modern Jazz Quartet. He wrote music for the Benny Goodman Orchestra that recorded in Britain and for Jack Parnell's ATV Orchestra.

Harvey joined Humphrey Lyttelton's band as its pianist and arranger, staying from autumn 1963 until 1972. He qualified as a teacher and became assistant music master at Haileybury College in Hertford, from 1969 to 1985. He rose to the forefront of jazz education in Britain and stayed there for several decades while continuing to play in a variety of jazz groups. He taught at the City Literary Institute in London and at various summer schools. He worked for the Arts Council of Great Britain and provided training for teachers, working in colleges and schools. From 1985 to 2003 he was Head of Jazz Studies at the London College of Music and Director of the London College Big Band. "The whole thing about teaching arts, and particularly jazz," he said, "is that you're not actually teaching them to play, you're teaching them how to teach themselves."

He taught at the Royal College of Music in 2004 and directed its big band. He was also an external examiner for the Trinity College of Music. Over the last years of his life he continued to compose and led his own big band for his own pleasure and for the benefit of the students who made up its ranks.

In 1974 he published Teach Yourself Jazz Piano and the book went into half a dozen editions. His Jazz in the Classroom: Practical Sessions in Jazz Improvisation appeared in 1988.

Edward Thomas Harvey, trombonist, pianist, arranger, composer and teacher: born Blackpool 15 November 1925 (twice married: two daughters from first marriage); died Twickenham, London 9 October 2012.