There is solid evidence that Liverpool were the first to sing "You'll Never Walk Alone" in the year 1963.
See:
Which_soccer_club_was_the_first_to_sing_You'll_Never_Walk_Alone
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No, not entirely. Liverpool and Celtic sing the song. Man United sing the tune, with words that insult Liverpool or Man City. Also, some teams sing 'Sign on, sign on' in the same tune which can get easily mixed up in recordings.
Now used by the Liverpool FC faithfull as their anthem You'll Never Walk Alone is actually a show song from the 1945 Rodgers and Hammerstein musical Carousel.
It was later sung by Nina Simone in1958 then Gerry and The Pacemakers in 1963.
Liverpool currently sing it at their matches, but how you have categorized it leads me to believe that the answer is Manchester United.
Neither, Luton did. But between Liverpool and Celtic, it was Celtic.
Hope this helps.
Liverpool. The song 'You'll Never Walk Alone' is not associated with Manchester United.