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There really won't be any Beatles music in the Beatles episode
(www.empireonline.com)
A good old fashioned Doctor Who Community
IIRC I think in some bit of extended lore it says that the Doctor can't go to any more Beatles gigs because there's already some version of themselves at every single one so it would be a time paradox lol.
Also in 2020 someone made an entire David Bowie biopic without having the rights to any Bowie music at all!