Born in Rome to an Italian father and a Maltese mother, Andrew Grima moved to London as a child. After serving in the Royal Engineers during World War II, he joined his father-in-law's jewelry firm, H.J. Company, where he began to revolutionize the traditional aesthetics of the trade. His breakthrough came in the 1960s, when his bold, avant-garde designs gained significant traction among the British elite and the royal family.

Grima’s signature style involved the use of textured, hand-beaten gold and the incorporation of rough, uncut crystals and gemstones, moving away from the rigid, formal settings of the era. His work often featured organic, abstract shapes that prioritized artistic expression over the traditional display of gemstone value. He was a frequent recipient of the De Beers Diamond International Award, cementing his status as a leading innovator in the field.

Today, Grima’s pieces remain highly sought after in the secondary market and at major auction houses. His legacy continues to be recognized for its contribution to the modernist movement in jewelry, with his designs frequently appearing in high-profile fine jewelry auctions in London and beyond.