While still studying at Edinburgh University, he began his career writing music for various Cambridge Footlights shows including the sketch show Grow Up, which enjoyed a successful run at the Edinburgh Fringe Festival. He then went on to form part of the team behind the soundtrack for the BAFTA-nominated feature film Black Pond. The film received multiple award nominations, as well as winning the 2012 Evening Standard British Film Award for Most Promising Newcomer.
Recent credits include the BBC's The Following Events are Based on a Pack of Lies, for which Arthur won his second Ivor Novello Award in 2024, and HBO's Landscapers, for which he won his first in 2022. Other credits include Sharon Horgan’s 6-part comedy drama Woman on the Verge, co-written with Lorna Martin and set in Dublin; and the 6 x 30 minute series Ghosts for BBC1. Arthur worked on two series of the Channel 4 comedy/drama series Flowers, produced by Kudos and starring Olivia Colman and Julian Barratt. Helping to create a dark and eerie world with his use of strings, piano and the occasional chant in backwards English, his score for the first series won him the 2016 RTS Craft & Design Award for Best Original Music.
In 2021 Arthur scored the feature film The Electrical Life of Louis Wain directed by his brother Will.
Alongside his film and TV work, Arthur also fronts and writes for the indie band Arthur In Colour. They released their debut EP Malatrophy EP in 2012, receiving an 8/10 review from Neon Filler and 4/5 from Music Muso. In June 2017, they released their debut album Nocturnalium.
“There was a lot going on in this score and the music effectively became another character in the show with a sense of quirkiness and drama – which is hard to pull off, but done so with aplomb in this winning entry.” - RTS Awards Jury on Flowers.