Marber was born and raised in a middle-class Jewish family in Wimbledon, London, the son of Angela (Benjamin), a theatre secretary, and Brian Marber, a technical analyst. He was educated at Rokeby School, St Paul's School, Cranleigh School, and Wadham College, Oxford where he studied English.


After working for a few years as a stand-up comedian, primarily as part of a comedy double act with author Guy Browning, Marber became a writer and cast member on the radio shows On the Hour and Knowing Me, Knowing You, and their television spinoffs The Day Today and Knowing Me, Knowing You... with Alan Partridge. Amongst other roles, Marber portrayed hapless reporter Peter O'Hanraha-hanrahan in both On the Hour and The Day Today, and was involved in a dispute with the comedians Stewart Lee and Richard Herring, who had written for On the Hour, about who had invented the character. Lee and Herring's TV show Fist of Fun would later make several references to their feud with Marber, calling him a "Cornish curmudgeon". In Stewart Lee's 2010 book, How I Escaped My Certain Fate, Marber is referred to as a "new Shakespeare". Marber reunited with the Knowing Me, Knowing You team in 2003 to record commentaries for the DVD release of the show. He also contributed some new in-character audio material to the DVD release of The Day Today in 2004.

He co-writes Bunk Bed for BBC Radio 4, which he created with Peter Curran. It was first broadcast during April 2014, with the fifth series broadcast in 2018, with special guest Jane Horrocks.