In November 2016, he was in a "Read Not Dead" performance of Beaumont and Fletcher's The Coxcomb at the Sam Wanamaker theatre on Bankside.
In 1990, he appeared as a doctor in the first episode of the comedy Keeping Up Appearances (entitled "Daddy's Accident"), and has also featured in episodes of numerous TV series, including The Bill, Casualty, EastEnders, Midsomer Murders and Doc Martin.
In 2013, he played the character of Peter Bachman in several episodes of the TV series Love and Marriage, including "The Elephant in the Room", "Secrets & Lies", "Alarm!"
Alexander's radio credits include the role of Mike in Westway, the BBC World Service soap opera which ran from 1997 to 2005,[2] and the role of Doc de Salis in the BBC dramatisation of the John le Carré novel The Honourable Schoolboy.
In 2022, he appeared as recurring character Doug in Catherine Tate's six-part mockumentary sitcom Hard Cell, released on Netflix.