He went to England at 19, in part because of Britain's wider career opportunities, but also to study informally with the great horn virtuoso Dennis Brain. Tuckwell also credits listening to the recordings of jazz trombonist Tommy Dorsey with shaping his idea of brass sound. During his LSO years he appeared regularly as a soloist, and in 1968 he left the orchestra to pursue a career exclusively as a horn soloist. He toured and taught widely all over the world, and is responsible for the commissioning of works that have become important addition to the horn repertory, including compositions by Gunther Schuller, Oliver Knussen, Richard Rodney Bennett, Thea Musgrave, and Ian Hamilton.
He was the first President of the International Horn Society (1970-1976) and served another term from 1992-1994, and is now a member of its Advisory Committee. He has worked diligently to advance horn playing and has worked on instrument design with makers such as Holton and Lawson. He was professor of horn at the Royal Academy of Music in London (1962-1972), Artist-in-residence at New Hampshire's Dartmouth College, Pomona College in California, and the Stratford Festival in Ontario. Tuckwell is also a noted editor of horn music and has authored two books on the techniques of horn playing.
In 1982 he helped found the Maryland Symphony Orchestra, serving as its music director into 1998. He was also music director of the Tasmanian Symphony Orchestra in Hobart, Australia. He also frequently appears as a guest conductor and has recorded an album of Wagner overtures. In 1992 Tuckwell was granted permanent U.S. residency under the new "Extraordinary Ability" immigration category, and became a U.S. citizen in 1997. He retired from professional horn playing in 1996, at the age of 65. He continues to conduct and teach, and works with promising youngsters at the Kendall Betts Horn Camp, Lyman, NH.