Markham may be best known for her solo flight across the Atlantic, from England to North America in 1936.

When Markham decided to take on the Atlantic crossing, no pilot had yet flown non-stop from Europe to New York, and no one had made the westward flight solo, though several had died trying. Markham hoped to claim both records. On 4 September 1936, she took off from Abingdon, southern England. After a 20-hour flight, her Vega Gull, The Messenger, suffered fuel starvation due to icing of the fuel tank vents, and she crash-landed at Baleine Cove on Cape Breton Island, Nova Scotia, Canada. She became the first person to make it from England to North America non-stop from east to west and was celebrated as an aviation pioneer.

Markham chronicled her many adventures in her memoir, West with the Night, published in 1942. Despite strong reviews in the press, the book sold modestly, and then quickly went out of print. After living for many years in the United States, Markham moved back to Kenya in 1952, becoming for a time the most successful horse trainer in the country.