The Style Council was an amazing group of musicians who weren't tied to any one genre of music and could easily move between jazz, soul and pop. Their sound is timeless and they managed some truly memorable songs along the way. They influence many people to explore music beyond the sound of The Jam.
XTC released an amazing streak of records in the 80s. English Settlement > Mummur > The Big Express > 25 O' Clock > Skylarking > Psonic Psunspot > Oranges and Lemons
While XTC may not be a directly mentioned influence, they sure do get the tribute treatment often enough.