How about the Tony Hazzard song "Paul McCartney"? And along with the Aerovons already mentioned, the Tom Hartman b-side "A Little More" is very McCartney sounding.
Hey Paul, I thought of a few more that could maybe work. Some of these are more Macca-esque than others but I'll let you be the judge:
The Flame - Lady
The Flame - Don't Worry Bill
The Flame - Highs and Lows
The Flame - Dove
The Flame - Another Day Like Heaven
The Tremeloes - I Swear
The Tremeloes - By The Way
The Tremeloes - Me and My Life
Colours - Helping You Out
Colours - Where Is She?
Colours - I Think of Here (She's On My Mind)
Grapefruit - Lullaby
Octopus - I Say
Rainbow Ffolly - Goodbye
The Twilights - Bessamae
Tranquility - Thank You
Savage Grace - Turn Your Head
Klaatu - Sub Rosa Subway
Vaughan Thomas - Woman in the West
Vaughan Thomas - We Are The People
Some people might find the Hudson Brothers a bit cheesy(their TV show certainly was) but they could really write catchy Beatlesque pop songs:
Hudson Brothers - Spinning The Wheel
Hudson Brothers - Oh Gabriel
Hudson Brothers - Isn't It Lovely
Hudson Brothers - So You Are A Star
Hudson Brothers - With Somebody Else
Two tracks from Yellowstone and Voice's 1971 album on Regal Zonophone: 'Lonely Man and 'Thinking about you and me'. In fact the whole album is very Macca.