Finlay began his musical training as a choral scholar at St. Paul's Cathedral and started learning the French Horn aged 11. He was awarded a music scholarship to Hampton School where he studied the horn with Richard Kennedy. He studied at the Junior Department of the Royal College of Music from 2007 to 2010, winning the Angela Bull Memorial Competition, the Anthony Gray Horn Prize and the Freda Dinn and Ida Mabbett Prize, and was runner-up in the Peter Morrison Concerto Competition.

Finlay was a Foundation Scholar at the Royal College of Music where he studied with Simon Rayner, John Ryan and Roger Montgomery (natural horn) and graduated with a 1st class BMus honours degree. He is now on a Postgraduate year studying with David Pyatt, Chris Parkes at the Guildhall SMD with a scholarship.

As a soloist, Finlay was a Brass Finalist in the BBC Young Musician of the Year competition 2010, broadcast on radio and television, and has performed Mozart's 4th Concerto, Strauss' 1st Concerto, Schumann's Konzertstuck for Four Horns and Britten's Serenade for Tenor, Horn and Strings.

As an orchestral musician Finlay has played in most of the major concert halls in the UK, and prestigious halls across Europe, in cities including Lucerne, Paris, Madrid, Lisbon, Dresden, Frankfurt, Amsterdam, Munich, Vienna, Athens and Salzburg; playing principal horn with ensembles including the Gustav Mahler Jugendorchester, the European Union Youth Orchestra, the National Youth Orchestra of Great Britain, the Ealing Youth Orchestra and the University of London Symphony Orchestra, and with other groups including the London Sinfonietta Academy, and the Aldeburgh World Orchestra.

He has also played professionally with the Konzerthausorchester Berlin, the Orchestra of the Royal Opera House, the Aurora Orchestra, London Symphony Orchestra, CBSO, BBC Philharmonic & Bournemouth Symphony Orchestra.