Adore demo, new Beatles song (4,2,2)

I believe the answer is:

love me do

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'beatles song' is the definition.
I know nothing about this answer so I cannot tell whether this works.

'adore demo new' is the wordplay.
'adore' becomes 'love' (I've seen this before).
'new' indicates an anagram.
'demo' with letters rearranged gives 'medo'.
'love'+'medo'='LOVE ME DO'

Can you help me to learn more?

(Other definitions for love me do that I've seen before include "Song - moved Leo (anag)" , "number in the sixties" , "first disc" , "Lyric" .)

I've seen this clue in The Telegraph.

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