Not the same League, though they were in the
Human League
Popular culture is part of a rounded general knowledge. Lack of familiarity puts you at risk of sounding like the stereotype of the High Court Judge.
There is much to value and cherish in our popular cultures - cinematic, musical, literary and televisual. I admit that I was living in the very centre of new British music of the early 80s, but it seems inconceivable for someone with even the briefest of access (via, say, the reviews in the Guardian) not to have even heard of Heaven 17.
They should be known beyond the realm of electropop, of course. Firstly, the name is a direct reference to A Clockwork Orange by Anthony Burgess, and secondly (and shame on you for not knowing this, Wow) their single (We Don't Need This) Fascist Groove Thing was banned by the BBC (well, by some DJs, but it barely got any airplay to speak of) for its overt left-wing lyrics and political nature - a distinction it shares with, for example, Ireland for the Irish by Paul McCartney.