Simpson's other great passions were astronomy (he was a member of the British Astronomical Association and – unusually for an amateur – was made a Fellow of the Royal Astronomical Society) and pacifism, specifically addressed in the title of his Tenth String Quartet, "For Peace". He was awarded many honours, including the Carl Nielsen Gold Medal, 1956 (for his book "Carl Nielsen, Symphonist", published in 1952), and the Medal of Honor of the Bruckner Society of America, 1962. He refused appointment as a Commander of the Order of the British Empire in 1980.