Born in Oxford, she made her acting debut in 2014 in the drama film The Falling.
Pugh gained recognition in 2016 for her leading role as a violent young bride in the independent drama Lady Macbeth, winning a British Independent Film Award.
After starring in the 2018 films King Lear and Outlaw King, she drew praise for her leading role in the 2018 miniseries The Little Drummer Girl.
Pugh was nominated for the BAFTA Rising Star Award that same year.
She was awarded the Trophée Chopard at the 2019 Cannes Film Festival.
In 2021, she starred as Yelena Belova / Black Widow in the Marvel Cinematic Universe superhero film Black Widow and the Disney+ miniseries Hawkeye.