Patel was born in Wembley, North West London. His parents are pharmacists. He completed his secondary education at the City of London School.
Patel graduated with a Bachelor of Arts in English from the University of Warwick in 2007. During his time at university, he discovered acting and played Othello in a student production. After graduating, Patel went on to train at the Guildhall School of Music and Drama, graduating in 2010. He was awarded the school's gold medal for Acting that year.