As I've said, we didn't have cable during MTV's formative years. But this thing played everywhere else during that time... Don Kirshner, Solid Gold, Video Rock (a local show), Kenny Everett's syndicated show from Britain...
If I'm not mistaken, it was also featured on a commercial for MTV ("I Want My MTV!") that let us commercial TV-watching slobs see what we were missing.
Of course, Madness was no one-hit wonder.