His first acting role was in the 1984 television series The Gentle Touch. He has since appeared in several television series including May to December, Minder, Only Fools and Horses, Nightingales, Murder in Mind, Press Gang, London’s Burning, Sean’s Show, Inspector Morse Driven to Distraction 1989, One Foot in the Grave, Red Dwarf, A Touch of Frost, The Bill, Le Café des Rêves, Sea of Souls Doc Martin, The Thin Blue Line and has appeared in the films Vera Drake (2004), The Aryan Couple (2004), The Illusionist (2006) opposite Edward Norton, and Dad Savage (1998) with Patrick Stewart. Wood starred in the 1989 Yellow Pages TV Advert, entitled “Party Party” and, until 2015, was the voice of the GEICO gecko advertisements on American television. Wood also featured alongside Cobent CTO and ex-Metal Hammer journalist Tony Dillon as part of a team presenting Click, a computer games magazine on VHS video in the early 1990s. In 1989, Wood appeared in Only Fools and Horses as an assistant for Rodney Trotter (Nicholas Lyndhurst), in the episode The Jolly Boys’ Outing. In the 8th series of Red Dwarf he played Kill Crazy, a prison inmate. Wood also played the eldest son, Dougie, in sitcom family The Wilsons.

In March 1990, Wood portrayed the role of Jackson in the BBC soap opera EastEnders, a minor character who met Diane Butcher (Sophie Lawrence) while she was sleeping rough on the streets of London. Wood was later cast to play the regular character Max Branning from June 2006 to date. In 2014, Wood took part in the 12th series of Strictly Come Dancing. He was partnered with Janette Manrara, reaching the semi-final. In May 2015, Wood announced that he would be taking a year-long break from EastEnders. Wood said “I have been at EastEnders for nine years and I feel the time is right to give Max a break. It won’t be for too long as I shall be back next year to see Max face another chapter of drama.”

Wood is a fan of Tottenham Hotspur and took part in the 2007 Great North Run. He lives with his wife, Alison, whom he married in 2001, and their two children, Buster and Amber.

In January 2018, Wood started hosting a boxing podcast, Pound for Pound, with Spencer Oliver. In September 2020, it was announced that Wood would be departing from the cast of EastEnders after fifteen years in the role, with Max being written out as part of an “explosive exit”.

In January 2019, it was announced that he would be running the London Marathon with some of his EastEnders co-stars for a Dementia campaign in honour of Barbara Windsor.