Ian Dury and The Blockheads had several hit singles, including "What a Waste", "Hit Me With Your Rhythm Stick" (which was a UK number one at the beginning of 1979, selling just short of a million copies), "Reasons to be Cheerful (Part Three)" (number three in the UK), and the rock and roll anthem "Sex and Drugs and Rock and Roll", often credited with introducing the phrase to the language.

Dury's lyrics were a unique combination of lyrical poetry, word play, acute observation of British everyday life and scatalogical humour. The Blockheads' eclectic sound was drawn from their many musical influences which included jazz, rock and roll, funk and reggae, not to mention Dury's love of music hall.

The band started when Dury had a chance encounter in a musical instrument hire shop with guitarist Chaz Jankel. Jankel took Dury's lyrics, fashioned a number of songs, and they began recording with drummer Charley Charles, bassist Norman Watt-Roy and the former Kilburns saxophonist Davey Payne. An album was completed, but major record labels passed on the band. However, next door to Dury's manager's office was the newly formed Stiff Records, a perfect home for Dury's maverick style. The classic single Sex and Drugs and Rock and Roll marked Dury's Stiff debut and this was swiftly followed by the album New Boots and Panties, which was to eventually achieve platinum status.

It wasn't until October 1977 that Dury and his band started to go out as Ian Dury and the Blockheads, when the band signed up for the Stiff "Live Stiffs Tour" alongside Elvis Costello And The Attractions, Nick Lowe, Wreckless Eric and Larry Wallis. The tour was a success and Stiff launched a concerted Ian Dury marketing campaign, resulting in the Top Ten hit What a Waste and the classic UK number one Hit Me With Your Rhythm Stick. The band toured to great acclaim throughout Europe.

The band's second album Do It Yourself was released in June 1979 in a Barney Bubbles-designed sleeve of which there were over a dozen variations, all based on samples from the Crown wallpaper catalogue. Another top ten single, Reasons to be Cheerful, kept Dury in the public eye.

In 1980 Jankel left The Blockheads to concentrate on a solo career and was replaced by former Dr Feelgood guitarist Wilko Johnson, who also contributed to the next album Laughter and its two minor hit singles.

Ian Dury And The Blockheads disbanded in 1981 after Dury secured a new recording deal with Polydor Records through A&R man Frank Neilson, choosing to work with a group of young musicians which he named The Music Students and recorded the album Four Thousand Weeks' Holiday. This album marked a departure from his usual style and was not as well received by fans for its American jazz influence.

The Blockheads reformed several times before Ian Dury's death, most notably to play a series of benefit concerts for Charley Charles.