The Harry Fox Agency licensing site, songfile.com shows a song called "Illegal, Immoral, and Fattening" written by H. Kaylan and M. Volman and recorded by Flo and Eddie. Probably not the same song, but interesting. I see also that there's a Ewan MacColl song titled "Legal Illegal," and I'm sure that has nothing to do with being immoral and fattening...
-Joe-