Bazalgette was the lead guitarist in the 1980s rock band "The Vapors", whose hit "Turning Japanese" remains a popular one-hit wonder. He later became a film editor, television producer, and director. In 2003, the BBC commissioned a seven-part documentary series called "Seven Wonders of the Industrial World". Edward Bazalgette directed and produced the documentary "The Sewer Ship", which depicted the design of his great-great-grandfather Sir Joseph Bazalgette and the design of London's sewers. His third cousin Peter Bazalgette later presented a show for "Five" called "The Great Stink". He also directed two drama-documentaries for the BBC - Genghis Khan (2005) and Hannibal - "Rome's Worst Nightmare" (2006).

He also directed episodes of EastEnders and Holby City, as well as location films for Top Gear. In 2013 he directed The Guilty, and in 2014 Poldark with Will McGregor. In 2015 he directed two episodes of the ninth series of "Doctor Who" ("The Girl Who Died" and "The Woman Who Lived"), as well as "Doctor's Meditation", a prequel to the series. He also directed the 2016 "Doctor Who" Christmas special "The Return of Doctor Mysterio". In addition, he directed the first three episodes of the Doctor Who spin-off Class in 2016.