(Manfred Mann - Not your average grab-bag of pretty faces)
During the first couple of years of the British invasion (1964-1966), one of the consistent hit makers were Manfred Mann. They turned out some memorable music and were one of the first British bands to record Dylan material "With God On Our Side", and it served them very well. Their second Dylan track, "If You Gotta Go, Go Now" (the one we've got here), did great in the UK - hitting at #2 before some of the lyrics and their implications were discovered and promptly banned from radio airplay. It was released here in the States, but as a B side so there was little, if any controversy because radio never played B-sides.
Despite that, Manfred Mann did very well and weathered some personnel changes before the band split up and resurfaced as Manfred Mann's Earth Band.
But this is 1965 and none of that has happened yet.