During the First World War, Markham served with the Royal Garrison Artillery on the Western Front and was awarded the Military Cross.[3]
He entered the British Civil Service
in 1921, joining the Admiralty. From 1936 to 1938 he served as Principal Private Secretary to successive First Lords of the Admiralty, Samuel Hoare (1936–1937) and Duff Cooper (1937–1938).[4]
In December 1940 Markham replaced Sir Archibald Carter as Permanent Secretary of the Admiralty, a position he held throughout the Second World War and until he was compelled to step back from his duties in October 1946 owing to ill health.[3]
He died at Margate on 14 December 1946, aged 49.[3] Tributes were paid in the House of Commons, including by the Parliamentary and Financial Secretary of the Admiralty, John Dugdale, who praised Markham's “outstanding ability and devotion during five of the most strenuous years in the history of the Navy. It would be difficult, I think, to find a more brilliant, fair-minded or charming civil servant. His death, at the early age of 49, has been a blow not only to the Admiralty, but to the entire Civil Service, and one which I, personally, have felt very keenly”.[5]
