It was the early 60’s. They probably had never heard of I Love Lucy. It was a different time. I would highly doubt American sitcoms were on British television.
We got I Love Lucy, and several of the classic sitcoms of the period. To be honest, many of them werent popular, as we found the likes of Ozzie and Harriet or The Andy Griffith Show far too saccharin and cutesy for the British sense of humour.
The favourite then (and remains so) was ‘Bilko’/’The Phil Silvers Show’, which British viewers, critics and comedians loved and still do. It far better suited our cynical sense of humour.
British TV in the 50’s and 60’s showed plenty of US tv, from drama to pop music, cop shows to sci fi.
British TV from the mid 50’s to now, has always shown plenty of US tv, a lot of it primetime (or peaktime as we used to say). Far more than than the reverse.
I was not implying that the Beatles were influenced by I Love Lucy. It’s the fact that the song is mundane and was considered appropriate for a sitcom gag ten years before the Beatles recorded it.
Oh what I would have given to hear the Beatles do a cover of "Cuban Pete."