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John Lennon repeatedly refers to himself as "working-class," in this film and elsewhere in his public comments and writings. One could argue, I suppose, about the specific circumstances of his upbringing. The aunt and uncle who raised him were not poor, and could be construed as clinging to the underside of the middle class, if only just. He did not come from anything like the kind of stable, middle-class English family life that, say, Mick Jagger did.
Lennon's father was a merchant seaman and his mother was a housewife who had four children by three different men. Both of them abandoned him. I suspect those roots were what Lennon meant by the term "working-class," and it sounds adequate enough for me.
Next time, come here with some better argument than "you ignorant Yank," please.