Brandreth was born in Wuppertal, Germany, where his father, Charles Brandreth, was serving as a legal officer with the Allied Control Commission. After having moved to London with his parents at the age of three, Brandreth was educated at the Lycee Francais Charles de Gaulle (as it is called today), Bedales School, where he met his friend Simon Cadell, and New College, Oxford. He was President of the Oxford Union in Michaelmas Term, 1969 and edited the university magazine Isis. He was described in a contemporaneous publication as "Oxford's Lord High Everything Else".

In the 1970s he hosted the ITV children's show Puzzle Party.  Brandreth has appeared on Countdown more than 300 times in Dictionary Corner, making more appearances than any other guest, including Carol Vorderman's final episode in 2008. He also appeared on TV-am. He was known for his collection of jumpers, of which some were sold in a charity auction in 1993.  In 2006, he appeared on the television series That Mitchell and Webb Look, satirising his appearances in Countdown's Dictionary Corner on the fictional game show "Numberwang". In 2007, he guest-starred in the Doctor Who audio play I.D. In July to August 2009, he hosted the game show Knowitalls on BBC Two. In April 2010, he appeared on BBC Radio 4's Vote Now Show. He also makes a cameo appearance as himself in Channel 4 sitcom The IT Crowd in the episode "The Final Countdown".  A frequent guest on BBC television panel shows, he has appeared on three episodes of QI and six episodes of Have I Got News for You. He has also appeared in episodes of Channel 5's The Gadget Show and is a contributor to the BBC's early evening programme The One Show. He has appeared in two episodes of the TV adaptation of Just A Minute as part of the show's 45th anniversary. In 2013, he was a guest on the Matt Lucas Awards.  He appeared on Room 101 in 2005, while Paul Merton was host, successfully banishing the Royal Variety Performance and the British honours system into Room 101, saying that he would never accept an honour himself. In 2013, he clarified this position, stating that he had "no fundamental objection to the honours system" and that he selected the honours system for Room 101, as he could "tell funny stories about it".

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