Hassall was born in London and educated at Brighton College. He is the son of John Hassall and brother of Joan Hassall, who engraved the title page of his book of poetry, Devil's Dyke, published in 1936. Hassall married the actress Eve Lynett with whom he had a son and a daughter, the actress Imogen Hassall.

Hassall was an experienced actor serving as Ivor Novello's understudy in a minor London drama when Ivor Novello invited him to provide the lyrics for a new musical. Their successful collaboration for Glamorous Night (1935) ("Shine Through My Dreams", "Fold Your Wings") began a fifteen year partnership that included six long-running hits. ('Perchance to Dream' the other hit which Novello wrote during this period, had lyrics by Novello himself). While their musicals delighted West End audiences, they were judged "too British" for America. Jeremy Northam, who played a character based on Ivor Novello in the 2001 Robert Altman movie, Gosford Park, sang "I Can Give You the Starlight" from The Dancing Years, Hassall's and Novello's 1939 musical.

During World War II in 1940, Hassall served in an anti-aircraft gun emplacement with editor John Guest, architect Denys Lasdun, and socialite Angus Menzies. A man of many talents, he recorded a record album entitled Great Voices Read Poetry (1954-1955) along with Richard Burton, Dame Peggy Ashcroft, John Gielgud, Robert Hardy, and Anthony Quayle. Hassall's contributions included: Upon Westminster Bridge, Daffodils, and Ode: Intimations of Immortality by William Wordsworth; and Death Be Not Proud by John Donne.

Hassall lived at Tonford Manor, a house with a mediaeval stone tower situated by the River Stour on the outskirts of Canterbury. He delighted in its fine prospect and had a road named after him in the community. At Thanington Church nearby is a small pane of glass engraved in his memory. Shortly before his death in 1963, Hassall spoke about the first Stour Music Festival, saying:

The shared experience a communion between listener and performer impossible in a great assembly (which) means the restoration of a large body of music to the private salon or to the church where it originally belonged. With the appropriate setting and a perceptive audience of proportionate size, the work will not only sound, but feel right.

Hassall died on a train at Rochester, Kent on 25 April 1963 after suffering a heart attack whilst running for the train to see his daughter play at the Royal Opera House. He was 51.