At age 16, Chowdhry made his acting debut in the 1988 film, Madame Sousatzka with Shabana Azmi and Shirley MacLaine.
Chowdhry was born and brought up in Bristol, England. In 1994 he graduated from Imperial College, London, earning a 3-year degree in biochemistry with 2:1 honours.
His next major role was as I.T. Teacher Kurt McKenna in the successful comedy show Teachers in 2001–2003, and is also well known for playing PC Sanjay Singh in Dalziel and Pascoe. He also appeared as a possible rapist in Judge John Deed.
On 30 October 2005, he appeared on stage at the Old Vic theatre in London in the one-night play Night Sky alongside Christopher Eccleston, Bruno Langley, David Warner, Saffron Burrows and David Baddiel. In 2005 he made a guest appearance in Doctor Who, then starring Christopher Eccleston as the Doctor. In 2006, he appeared in the BBC Three drama series Sinchronicity, playing Mani.
In 2009, he appeared in two episodes of the Channel 4 series Free Agents and featured in Skellig. In 2010, he starred in the BBC television pilot Reunited, playing Danny.
He played Anwar in the critically acclaimed 2015 BBC TV series Doctor Foster and in 2016 he played Sonny Desai in Series 18's first episode of Midsomer Murders.
He portrayed Nodin Chavdri in the 2017 film Star Wars: The Last Jedi.
