Smith Brindle was born in Cuerdon, Lancashire. He began learning the piano at the age of six, and later took up the clarinet, saxophone and guitar (and won a Melody Maker prize for his guitar-playing). Under pressure from his parents, he began to study architecture. At the time, he was interested in jazz, and played saxophone professionally for a while alongside his studies. On attending an organ recital at Chester Cathedral in 1937, however, he was inspired to take up both the organ and composition. He spent most of the war serving in Africa and Italy as a sapper. It was during this period that he rekindled his interest in the guitar, an instrument for which he wrote an enormous amount of music.
After the war, Smith Brindle returned to composition. He submitted a Fantasia Passacaglia (1946) for an Italian composition competition, and won first prize. From 1946 to 1949 he studied music at the University College of North Wales in Bangor. He went to Italy in 1949 to continue his studies. Here his teachers included Ildebrando Pizzetti and Luigi Dallapiccola.
Although he wrote for many instruments, Smith Brindle was perhaps best known for his solo guitar music, especially El Polifemo de Oro (1956), written for Julian Bream, as well as five sonatas (1948, 1976, 1978, 1979), Variants on two themes of J. S. Bach (1970), Memento in two movements (1973), Do not go gentle... (1974), November Memories (1974), Four Poems of Garcia Lorca (1975), Preludes and Fantasies (1980) and The Prince of Venosa (1994). His only opera, The Death of Antigone, premiered at Oxford in 1971.
Smith Brindle was an expert on the music of 20th-century Italian composers such as Luigi Dallapiccola, Ildebrando Pizzetti and Bruno Bartolozzi (he studied with all three). He also wrote a technical book "Serial Composition"(1966). He played many instruments, but was particularly fond of the guitar, organ and saxophone.