That's true of their early stuff
But in the '80s, once their core of Smith, Scanlon, and Hanley were cemented, they had moved away from political stuff to more cryptic and sometimes absurd. Compare "The NWRA" in 1980 to "Garden" from three years later. Both long atmospheric songs, but the latter is completely apolitical. Later on the lyrics became incomprehensible yet clever, and by the end just incomprehensible.
That's just a long-winded way to say that they stopped being "wacky English proletatiat idiots" in around 1982, before -- for many people -- the "true" Fall had even gotten started.