An only child, Challis was born in Bristol but brought up in South East London. His father James Alec, from Sheffield, was a Civil Servant. Challis attended the state boarding Ottershaw School near Woking, Surrey. Upon leaving school he worked as a trainee estate agent before becoming a professional actor. An early television role, in 1969, was in the controversial gangster drama Big Breadwinner Hog, and between 1971 and 1975 he made regular appearances in Z-Cars as Sergeant Culshaw.

Challis appeared on the Channel 4 mockumentary television programme Brass Eye, where he was tricked into believing Clive Anderson had been shot by Noel Edmonds. On BBC radio, he played an interrogator in the play Rules of Asylum by James Follett, broadcast by BBC Radio 4 in 1973. He also played Dibden Purlew in Getting Nowhere Fast from 2001 to 2004.

Challis is currently married to his fourth wife Carol. They married in 1993 and live in the former grange house of Wigmore Abbey, Wigmore, Herefordshire. Challis has no children.

The outdoor scenes of The Green Green Grass were filmed at his then home, surrounding fields and local villages. Four series were broadcast by BBC One from 2005–2009. In the 2008 series of Last of the Summer Wine he guest-starred as a fake jewel thief, trying to impress the ladies.

Challis has had a number of stage roles. He starred in pantomime at the Plaza Theatre in Stockport as Captain Hook in Peter Pan. He also appeared in pantomime at Weston Playhouse in winter 2011–12 playing Ebenezer in Aladdin and as King Rat in Dick Whittington at the Plaza Theatre in Stockport over Christmas 2013 and New Year 2014. In 2006 he took a cameo role in BBC's The Impressionists as Station Master Garre Saint Lézasr. He appeared alongside Christmas enthusiasts Paul Toole and Chris Elliott in the Channel 4 documentary King Of Christmas Lights, which aired on 19 December 2011, switching on the Christmas Lights at Manning Close in Wells, Somerset, on 30 November. He also flicked the switch in Weston Super Mare on 1 December 2011. In 2013 Challis occasionally contributed to the Hitchhiker's Guide To The Galaxy Live Tour as the narrator.

Challis has written two volumes of autobiography, Being Boycie and Boycie & Beyond. From April 2012 he embarked on a book tour to promote Being Boycie, starting at Waterstones in Uxbridge, and the same year became the narrator of the National Geographic Channel series Strippers: Cars for Cash.

In 2014, Challis began a theatre tour of his one-man show titled Only Fools and Boycie, which charted his life before, during and after his time as 'Boycie'.

On 19 February 2016 Challis was cast in the role of Captain Peacock taking over the role originally played by the late Frank Thornton in a remake of Are You Being Served? The episode aired on BBC in August 2016.