Mafham appeared in the play Linda, written by Penelope Skinner and directed by Michael Longhurst, which opened on 26 November 2015 at the Royal Court Theatre in London. He played Neil, the husband of Linda, played by Noma Dumezweni who replaced Kim Cattrall after she left the production in the final week of rehearsals, citing "doctor's orders".
In spring 2015 Mafham played Antonio in The Merchant of Venice at Shakespeare's Globe Theatre. Jonathan Pryce played Shylock. The production was revived for a major tour in 2016, visiting New York, Washington and Chicago in the U.S. and several cities in China before returning to Shakespeare's Globe in October and culminating in a run in Venice at the Teatro Goldoni. The production received rave reviews.