He was educated at Winchester College and has a degree in history from Oxford University where he appeared in a number of student plays. During his studies he did a lot of stage performance, including touring Japan with an OUDS production of Love's Labours Lost. He then trained at the Royal Academy of Dramatic Art (RADA), graduating in 2005. Wyndham augmented his formal education by completing programmes such as: a camera acting course at BBC Elstree; earning the BASSC Certificate 1st class (distinction) armed and unarmed combat; and achieving the level of black belt (1st Dan) Shotokan Karate. He has many skills including period and Flamenco dancing, and sings baritone. His special interests include: athletics, films, travel, guitar and graphic design.
His first job as a professional actor was playing Silvius in Kenneth Branagh's adaptation of As You Like It while he was still at drama school. His other credits include an appearance in T4's girl-band soap Totally Frank as Ben, The Line of Beauty and Little Dorrit. He is currently shooting the BBC World War One medical drama The Crimson Field.
|2006||As You Like It||Sylvius|
|2007||Arn – The Knight Templar||Armand De Gascogne|
|2009||The Hills Run Red||Lalo|
|2005||Totally Frank||Ben||7 episodes in season 1|
|2006||The Line of Beauty||Wani Ouradi||Miniseries|
|2007||Maurice||Maurice||BBC Radio 4|
|2007||Rome||Maecenas||7 episodes in season 2|
|2008||Little Dorrit||Henry Gowan|
|2014||The Crimson Field||Miles Hesketh-Thorne|