Commissioned at the beginning of World War I, he fought at Gallipoli and served in Egypt before transferring to the Royal Flying Corps in September of 1916. During pilot training that year, he received only 22 minutes of dual instruction before he soloed for the first time on December 11.

Assigned to 56 Squadron in March 1917, he was assigned to A Flight underAlbert Ball, scoring his first victory during his first patrol over the lines on April 24, 1917. Flying the S.E.5a, Maxwell scored 20 victories before returning to England on October 21, 1917.

After serving as an instructor at Turnberry, he rejoined 56 Squadron in the summer of 1918, scoring 6 more victories during June and July. When the war was over, he joined the Stock Exchange but returned to service during World War II, attaining the rank of Wing Commander in the Royal Air Force. Maxwell's younger brother Michael also served in the RAF during World War II and became an ace.