I'd forgotten about Wet Wet Wet - that's a good example.
A few more:
Pet Shop Boys' "A Red Letter Day": 9-42-62-OUT
Embrace's "My Weakness is None of Your Business": 9-44-69-73-OUT
Super Furry Animals' "Ice Hockey Hair": 12-41-60-OUT
Chemical Brothers' "Loops of Fury": 13-OUT
Cliff Richard's "21st Century Christmas"
2-7-43-OUT
OK, it is Christmas related, but it's still remarkable.
"Come Play with Me" by Wedding Present
10-65-OUT
(though that was limited edition)
Prince - Kiss
Kiss - God Gave Rock 'n' Roll to You
Human League - Louise
Louise - Arms around the World
Smiths - Shakespear's Sister
Shakespears Sister - Stay
East 17 - House of Love
House of Love - Beatles and the Stones (which itself contains 2 group names!)
Aerosmith - Shut Up and Dance
Shut Up and Dance - Raving I'm Raving