Their first single, released by the new Two Tone label, "Prince Buster" was a runaway success breaking into the British top 20. Likewise their sophmore single, the ska instrumental "One Step Beyond" rose to #7, and their third "My Girl" topped that by going to #3. The trend became commonplace after that with the band's first 13 singles hanging around the tops of the charts. Madness were enormously popular in England right through the mid-80s, with maybe only The Jam being more loved by Brits.
Always the core of the group, Mike Barson's songwriting and keyboards gave the band an edge, as well as a different sound that set them apart from the rest of the two-tone movers and shakers like The Specials and English Beat. Barson left the band in '83, and while Madness still did well throughout the rest of the decade, the highest of heights were being left behind.
Here's a great sample of their quirkiness, cleverness, and overall musical genius. "In The Middle of the Night" dabbles with crime and fetish, something many of their songs touched upon though they also sang about politics and culture a fair amount. The keyboards, the trumpets, the guitar, it all just works so well. And the nuttiness of it all makes a song about an underwear theif more charming than creepy.