Markham was born in the village of Ashwell, in the county of Rutland, England, the daughter of Charles Baldwin Clutterbuck, an accomplished horse trainer, and his wife Clara Agnes (née Alexander) (1878–1952). She had an older brother, Richard Alexander "Dickie" Clutterbuck (1900–1927).

When she was four years old, she moved with her father to Kenya, which was then colonial British East Africa. He built a horse racing farm in Njoro, near the Great Rift Valley between the Mau Escarpment and the Rongai Valley. Markham spent an adventurous childhood learning, playing, and hunting with the local children. On her family's farm, she developed her knowledge of and love for horses, establishing herself as a trainer at the age of 17, after her father left for Peru.

Adventurous, independent thinking, and beautiful, Markham was admired and described as a noted non-conformist, even in a colony known for its colourful eccentrics. She was married three times, taking the name Markham from her second husband, the wealthy Mansfield Markham, with whom she had a son, Gervase. She had a public affair in 1929 with Prince Henry, Duke of Gloucester, the son of King George V, but the Windsors allegedly cut the romance short. She also had an affair with Hubert Broad, who was later named by Mansfield Markham as a co-respondent in his 1937 divorce from Markham. After her Atlantic crossing, she returned to be with Broad, who was also an influence in her flying career.

She befriended the Danish writer Karen Blixen during the years that Blixen was managing her family's coffee farm in the Ngong hills outside Nairobi. When Blixen's romantic connection with the hunter and pilot Denys Finch Hatton was winding down, Markham started her own affair with him. He invited her to tour game lands on what turned out to be his fatal flight, but Markham supposedly declined because of a premonition of her flight instructor, British pilot Tom Campbell Black.

Inspired and coached by Tom Campbell Black, Markham learned to fly. She worked for some time as a bush pilot, spotting game animals from the air and signaling their locations to safaris on the ground.

She also mingled with the notorious Happy Valley set.