Simpson's best known work includes, but is not limited to:

BRITAIN & IRELAND:
Ashridge GC, Eng (1938, redesign) / Ballybunion, Ire (1937, modifications to Old course) / Carlisle GC, Eng (1908) / Carlow GC, Ire (1937, modifications) / County Louth, Ire (1938) / Cruden Bay, Scot (1926, modifications) / Ganton, Eng (1934, modifications) / Hayling, Eng (1933, modifications) / Liphook, Eng (1922, with Arthur Croome) / Muirfield, Scot (1928, modifications) / Nairn, Scot (1920, modifications) / New Zealand GC, Eng (1929, modifications) / North Foreland, Eng (1913, redesign with Herbert Fowler) / North Hants, Eng (1930, modifications) / Royal Porthcawl, Wales (1933, modifications) / Rye, Eng (1932, modifications) / Sunningdale, Eng (1934, modifications to New course).

CONTINENTAL EUROPE:
Chantilly, Fra (1909, Vineuil/Old course) / Chiberta, Fra (1927) / Club du Lys, Fra (1929, Les Chenes course) / Deauville, Fra (1929, nine-hole Red course) / Fontainebleau, Fra (1909) / Hardelot GC, Fra (1934, Les Pins course) / Morfontaine, Fra (1927, Le Grand Parcours and Vallière courses) / Puerta de Hierro, Spain (1924 & 1945 modifications to Arriba course) / Royal Antwerp, Belg (1930, modifications) / Royal Belgique - Ravenstein, Belg (1928, modifications) / Royal des Fagnes - Spa, Belg (1930) / Royal Hainaut, Belg (1932) / Royal Malaga, Spain (1925) / Royal Sart Tilman, Belg (1938).

Simpson was one of the breed of gentleman amateur architects as opposed to a professional golfer or club pro turned designer. He was born into a wealthy mining family, and was always financially secure. Although not voluminous, Simpson's portfolio of work is still impressive, and ranks him as one of the most influential designers of the period between the two World Wars.

After attending Cambridge University and qualifying as a barrister, Simpson developed a keen interest in golf course architecture. His interest in architecture appears to have resulted from his membership at Woking GC, where Stuart Paton and John Low were revamping Tom Dunn's original design. The wealthy, eccentric and forthright Simpson did not need the money from his course design work, and although a barrister, rarely practiced law. Simpson often arrived at golf clubs in his chauffeur-driven Rolls-Royce, wearing a French beret. In the matter of his designs, he took a very direct approach to dealing with committees, which was unambiguous and frequently controversial.

In 1923 Simpson became one of the four founding partners in the golf course design firm of Fowler, Abercrombie, Simpson & Croome. Simpson struck out on his own in 1928, setting-up as Simpson & Co. His business became a direct rival to Harry Colt's firm of Colt & Company, on whose work Simpson was often unashamedly critical.

Simpson co-authored “Design For Golf” with Roger & Joyce Wethered. Published in 1929, the book remains one of the most under-rated texts on golf course architecture. Simpson was not a prolific golf course architect, perhaps because his manner could be both eccentric and offhand, and his fees were often substantially more than his competitors. In addition to his designs in Britain, much of his work was done in Ireland and on the European continent.