I've put together a group of music videos from around 1983-85 when a lot of great music was being creating in the UK. I used to listen to these songs on a college station broadcasting from Western Connecticut State University in Danbury, CT: WXCI. One of the station's programs was called "The Friday Night Dance Party." For your enjoyment I have tracked down songs that were played on that program back in that time period.
Howard Jones, "What is Love?" (released November 26, 1983)
Scritti Politti, "Wood Beez"
Frankie Goes to Hollywood, "Welcome to the Pleasuredome"
Bronski Beat, "Why"
Tears for Fears, "Shout"
Depeche Mode, "Master and Servant"
Talk Talk, "It's My Life"
Ultravox, "Dancing with Tears in my Eyes"
Pet Shop Boys, "West End Girls"
Dead or Alive, "In Too Deep"
Go West, "We Close Our Eyes"
Wide Boy Awake, "Billy Hyena"
Belouis Some, "Some People"
Blancmange, "Don't Tell Me"
Kajagoogoo, "Big Apple"
Re-Flex, "The Politics of Dancing"
Modern English, "I Melt with You"
Thompson Twins, "Doctor Dream"
Murray Head, "One Night in Bangkok"
Human League, "Fascination"
A few more added here since Friday night including "Wind Power" that Elliot suggested.
Thomas Dolby, "Wind Power"
Art of Noise, "Close to the Edit"
New Order, "Blue Monday"
Psychedelic Furs, "Ghost in You"
The Smiths, "How Soon is Now?"
Vitamin Z, "Burning Flame"

Salon.com
Comments
You MADE my night!
- es
Double thanks!
- Elliot
http://www.coverville.com/archives/2005/06/coverville_103.html
I can't BELIEVE you have One Night in Bangkok. Nobody even KNOWS that song anymore! :)
I would add Marc Almond, "Tears Run Rings"
http://www.youtube.com/watch?v=rGzU-GVNlqc
Peter Schilling, "The Different Story" (OK, German, but hey, he's European at least :)
http://www.youtube.com/watch?v=Ovyq19v5Y94
Faith No More, "We Care A Lot" (OK, not Brits, but it really needs to be in any complete 80s list :)
http://www.youtube.com/watch?v=FFEOmc8ZX6M
Jesus Jones, "Info Freako" (which we all thought was NYMPHO Freako)
http://www.youtube.com/watch?v=7FjVjt78iqk
Slade, "My Oh My" and "Run Run Away"
http://www.youtube.com/watch?v=hSZ2JZ6fw88
http://www.youtube.com/watch?v=bHoPYLQvnQM&feature=related
The Polecats, "Make a Circuit with Me"
http://www.youtube.com/watch?v=GA4foTap-WQ
I suppose Boomtown Rats' "I Don't Like Mondays" was too early (1979), but it fits style-wise.
http://www.youtube.com/watch?v=8yteMugRAc0
Jon Anderson and Vangelis, "The Friends of Mr. Cairo" (blew me away the first time I heard)
http://www.youtube.com/watch?v=6Ph8hNljOXE
Hipsway, "Honey Thief" (best dancing ever in a video ;)
http://www.youtube.com/watch?v=CPQwCrJ7LmE
Thompson Twins, "You Take Me Up"
http://www.youtube.com/watch?v=gqbbqzwTpyM&feature=related
And....that's probably enough.
Why yes, I am a bit obsessive about the 80s, why do you ask? ;)