Comper was born to Ellen Taylor of Hull and the Reverend John Comper as the eldest of five children. He was educated at Kingston College, Aberdeen, Glenalmond School in Perthshire and then went to the Ruskin School of Art in Oxford for a year. Working in for various established architects and stained-glass designers in London, he eventually formed a partnership with William Bucknall in London, 1888. Comper married Grace Bucknall in 1890 and they remained together until 1905.
Some of his most impressive work includes a line of windows in the north wall of the nave of Westminster Abbey; St Michael and All Angles in Inverness; the ciborium and House Chapel extention for the Society of St. John the Evangelist in Oxford (now St. Stephen's House) and the Lady Chapel at St. Matthew's in Westminster. This is just a small handful in the long list of his ecclesiastical commissions that are dotted around the country. His work also spread across the Atlantic with one major piece to note - the Leslie Lindsey Chapel of Boston's Emmanuel Episcopal Church. Comper designed its altar, altar screen, pulpit, lectern, dozens of statues, all its furnishings and appointments, and most notably the stained glass windows. In 1936-38 he designed "one of his most famous and original churches" - St. Phillip's Church at Cosham near Portsmouth.
St. Margaret's was a former Scottish Episcopal Church and was completed in 1907. It's described by Historic Scotland as "a remarkable example of a late Gothic Revival church", it is considered to be "one of the finest example of his (Comper) work and shows an expert knowledge of the components and proportions of the different phases of Gothic style ... His symbol, a strawberry, is a frequent motif". The church construction cost £8,000 and the first meteorological station in the village was at the top of the tower.
Comper is distinguished among other Gothic architects of that time as he re-introduced the 'English altar' frequently into his designs. This specific altar arrangement is surrounded by riddle posts. One of the finest examples of his medieval inspired altars is in Wymondham Abbey, Norfolk.
In his personal life, Comper lived in London with Grace from 1912. He had a studio close to Knights Hill which was tragically destroyed in World War II , and so he had to relocate to a outbuilding in his garden. Previously the outbuilding had been used by his son Nicholas Comper (1897 - 1939), to design aircraft. In 1950, Comper was knighted by King George VI. He died in December 1960 in the Hostel of God (now Trinity Hospice) in Clapham. His ashes are scattered under the line of windows he designed in Westminster Abbey.