Stephen Dodgson was born to a creative family in London. His parents were painters, and a distant ancestor was Charles Lutwidge Dodgson (better known as the artist Lewis Carroll). During the Second World War, he was conscripted into the British Navy from Stowe School before receiving his musical education at London's Royal College of Music (initially as a French Horn player): he would then spend 26 years teaching theory and composition there. He served for the first time at the BBC in 1957 and, as a presenter on a large variety of musical topics, would continue to provide background music for many of their dramatic productions and be one of the most recognized (and most loved) voices of the company.

The more than 250 works by Dodgson vary from songs and solo instrumental parts to chamber operas, choral music, and orchestral works on a wide scale. He was still realistic, even though his music was never predictable, mostly composing for musicians he knew and respected. For The National Youth Wind Orchestra, of which he was chairman for several years, he wrote a variety of distinctive works, and his involvement with the noted Philip Jones Brass Ensemble led him to write or organize an assortment of brass music. His marriage to the harpsichordist Jane Clark in 1959 cemented an obsession with Baroque music that infused many of his works; he had a specific association with three 'domestic' instruments, the recorder, guitar (fostered by Julian Bream), and harpsichord. Witty, gifted with a prodigious memory (he was an inveterate narrator), and his music is still honored by The Stephen Dodgson Charitable Trust with a compassionate spirit that shines through his works.