"It was Only a Hopeless Fancy" Song

On page 138 of 1984, Winston is walking through the proles' neighborhood, and he hears a woman singing a song created by a sub-section of the government, the Music Department, on an artificial instrument known as a versificator. The lyrics are "It was only a hopeless fancy, it passed like an April day, but a look and a word, and the dreams they stirred,they've stolen my heart away?" Does this mean the government uses music as propaganda? Does this even bear any significance, is Orwell trying to get a point across?

There is control over everything, the books that are read, the movies that are watched, so the government must obviously have control on the music that is listened to. But my question is, why were the proles singing it? And how? If they cannot afford telescreens, and the government does not care as much about them because they are uneducated, which means easy to control, why are they singing it?

My questions are, a.) how did the proles hear about this song? Are they totally cut off from the inner and outer parties? and
b.) what is the need for this group to be singing this song?