Leonard Alfred Boodle was educated at King's College School, London, and continued his studies at the Royal College of Science in London where he graduated as an associate (ARCS). He also went abroad for a year to study French and German. As a demonstrator in botany at the Royal College of Science for seven years he worked mainly on marine algae. He was elected a Fellow of the Linnaean Society in 1888. In 1889-1890 he collected marine algae along the South African coast from Cape Town to Knysna and presented his large collection to the British Museum (Natural History).
From 1897 Boodle concentrated on plant anatomy and in 1904 was appointed to the Jodrell Laboratory at Kew, where he was an assistant keeper from 1909 to his retirement in 1930. He published some 70 scientific papers during his career, mainly on the anatomy of plants, some of which dealt with species of southern Africa: In 1907 he contributed anatomical notes to a description by O. Stapf of Peglera capensis. The next year he and F.E. Fritsch translated from the German an extensive work by H. Solereder, Systematic anatomy of the Dicotyledons. In 1913 he described "The root and haustorium of Bottonia natalensis" in Kew Bulletin. The algae genus Boodlea (Siphoneae) was named in his honour.
Boodle carried out his research with the most meticulous care, but was extremely cautious in his conclusions. He was exceptionally modest and retiring.