Myles was born in London. Her mother, Jane (née Allan), works in educational publishing, and her father, Peter R. Myles, is a retired Church of England vicar in Isleworth, West London. Her maternal grandmother was Russian, and she refers to herself as "half-Welsh, half-Russian".
Myles grew up in Notting Hill, where her father served at the Church of St. George the Martyr, and attended Fox Primary School. At the age of eleven, Myles moved with her family to Isleworth and attended the Green School. Following success at her A-levels, she had been planning to accept a conditional place to study philosophy at Cambridge, but chose to pursue an acting career after being spotted by Julian Fellowes in a school play.