Godwin was born in 1904 in Bromley, Kent. He rowed for Great Britain in the 1924 Summer Olympics in Paris. He was affiliated with the Thames Rowing Club in Putney. He was coxswain for the men's eight. The Thames club won the Grand Challenge Cup at the Henley Royal Regatta in 1923, but only four members of that victorious crew, Ian Fairbairn, Godwin himself, Arthur Long, and Charles Rew, were present at the Paris Olympics. His team came in fourth in the Olympic competition. Godwin was again part of the Thames club team when they won the Grand Challenge Cup in 1927.