The promotional music video for “Come Dancing” was shot in November 1982 at Ilford Palais in Essex. The video was produced by Michael Hamlyn and directed by Julien Temple, with choreography done by Jim Cameron. Dave Davies later said of Temple, “Julian was such a posey sod, walking around in a fur coat like he was Orson Welles, even though he was only doing a promo video.” Local fans of the band appeared as the audience. The video was first broadcast in Britain in December 1982 on The Tube, a show on Channel 4, making its American debut on MTV on 25 March 1983.
In the video, the lyrics of “Come Dancing” are used as the storyline. Calling back to his youth, Ray starred as the “spiv” character who took the sister out to dance. Ray’s character, according to author Johnny Rogan, was inspired by the Davies brothers’ uncle, Frank Willmore, who Dave Davies described as “an old school kind of cockney”. The members of the Kinks were featured as the band performing at the palais at the end of the video, with the spiv character solemnly watching the performance. Temple said of this scene, “I was standing behind [Martin] Scorcese at a bar, and he was going on about that shot, saying it was one of his favorites ever. There’s a [Luis] Buñuel film, Simon of the Desert, where this guy who’s been suffering on his pillar in the desert in BC whatever ends up in some weird club in Mexico City in ’65. It’s a bit like that. [Ray] did it beautifully, the fact he’s so still and they’re all heaving around him. I think Ray could have been more of an actor. He has a great, deep sense of film.”
The band would revisit the spiv character Ray played in the video multiple times, such as in the music videos for “Don’t Forget to Dance” and “Do It Again.” According to Ray, the band’s 1986 album Think Visual was originally going to be a concept album centered on taking the character and putting him in the “environment of a video shop.” Ilford Palais was demolished in 2007 to make room for luxury flats, meeting a similar fate to that of the palais described in the lyrics of “Come Dancing.”