The first two lines are "Tea time won't be the same without my Donna / At night I lie awake and dream of Donna." I hadn't realized this before, but I think these lines' mentioning an absent Donna is an allusion to Ritchie Valens' "Donna." The first verse of Valens' "Donna" starts with the lines "I had a girl; Donna was her name / Since she left me, I never been the same." While one song describes the effect on the speaker/singer and one describes the effect on tea time, neither is "the same" because Donna is gone.
The next two lines in "Afternoon Tea" are "I think about that small café / That’s where we used to meet each day," and I think this alludes to Buddy Holly's "That's My Desire," specifically the second verse:
To meet where gypsies playBoth have a "small café" that's rhymed with "day." The next line in "That's My Desire" (which is the first line of the bridge) is "We'll sip a little glass of wine," so there's drinking involved there too, except it's wine instead of tea.
Down in some small café
And dance 'til break of day
That's my desire
Both "Donna" and "That's My Desire" pre-date "Afternoon Tea" by about a decade, so these allusions are possible from a chronological point of view, but I don't know enough about Ray Davies' influences to be certain that these are intentional references.