Peters was born in Stockport, England. By the age of 15, while still in school, he had written material for radio and TV shows including The Two Ronnies and The News Huddlines. After graduating from university with a law degree he worked at the High Court of Justice in London, and in his spare time worked as a reporter on Capital Radio's The Way It Is news magazine show. He then became a full-time journalist, winning a number of awards for his travel reporting. This became a series of travel specials called Wildfire on BBC Radio. In 1987 he won the Best Light Entertainment Writer Award at the New York Radio Festival for his series Around the World in Ninety Seconds. In 1997 he moved to Los Angeles, California. He lives with his partner in Hollywood, California.

Peters appeared for two seasons in the Travel Channel TV show Stranded with Cash Peters, and wrote the book Naked In Dangerous Places about his experiences on the show. He also presents a short segment on show business on Wednesday mornings every week on BBC Radio Five Live's Up All Night, with host Rhod Sharp, and appears as a commentator on American Public Media's Marketplace radio programme.

In 1979, Peters staged an elaborate April Fool's joke on Capital Radio's Sunday Soapbox, in which he went on-air as a concerned listener and ranted for several minutes about how disgusted he was about the government's plans to cancel the following two Thursdays. This so-called scheme was called Operation Parallax, and was the government's way of correcting errors that had occurred due to switching the clocks back and forth every year to account for British Summer Time. 48 hours had accumulated altogether, and these needed to be spent, so the following two Thursdays would be cancelled and the calendar would jump from Wednesday to Friday. As a result of this hoax being broadcast early on a Sunday morning, it fooled tens of thousands of Capital Radio's listeners, sparking panic. For a time, theatres cancelled their shows, airlines pulled flights, and emergency lines at Capital Radio and across London were jammed for hours. Operation Parallax was subsequently nominated by The Sunday Times as one of the top ten April Fool's jokes of all time.