After attending the Birmingham School of Art, Brockhurst entered the Royal Academy Schools where he was awarded the Gold Medal for Drawing – a medal he later sold in a moment of poverty - and a traveling scholarship in 1913.
During the 1920s Brockhurst was primarily an etcher, focusing on female portraits and using his first wife Anäis as his model. The numerous etched and painted portraits bear witness to the fascination of her brand of beauty; both physically and emotionally she became the embodiment of those dreams of fair women.” However, in 1928, when Brockhurst was appointed a visitor to the Royal Academy Schools, he met Kathleen Woodward, the sixteen year old student who was to supersede Anais in Brockhurst’s life as love, muse and later, wife.
His success as a portrait painter came after he was already well-established as an etcher, a career which reflected his skill as a draughtsman. His drawings, whether in watercolour, chalk, charcoal, pencil, ink or ink and wash, captured his subjects with a technique which was both instinctive and controlled, excelling in the representation of texture, such as skin, flesh, hair, lace, silk and embroidery.
In 1939 Brockhurst emigrated to America, living first in New York City and then New Jersey. There was no shortage of admirers and commissions for his meticulous technique and ability to convey a likeness. There have been exhibitions of his work at the National Portrait Gallery, London, the City Art Gallery Birmingham and Graves Art Gallery, Sheffield (1978), and more recently at the Georgia Museum of Art.