Alexander was born in London and started showing an interest in acting when his younger brother also began to work in the industry. Voice work became his focus for a couple of years and he voiced the title role in Claude for Disney Junior. Alexander has enjoyed success in British theatre including South Pacific in Concert at Cadogan Hall; Bodies at the Royal Court Theatre and most recently, young Macduff in Macbeth at the Barbican for the Royal Shakespeare Company. His television includes two series of The Reluctant Landlord opposite Romesh Ranganathan for Sky One.