On December 02 1963, the Beatles taped an appearance on the British Television show "The Morecambe and Wise Show" with hosts Eric Morecambe and Ernie Wise. This was taped at Studio C, Elstree Studio Center in Borehamwood. The purpose of this appearance was ostensibly to promote the new single and the new LP which had been released only a week and half previous in late November. There were three songs performed (not counting the last corny number with the hosts of the show).
The first song performed was the B-side to the latest British single entitled "This Boy". This features John on vocal although the verses feature all three Beatles singing in harmony. The next song featured on the show is from the LP "All my Loving" which has Paul singing and a George/Paul duet for the last verse. The Beatles finish the set with the A-side to the latest British single entitled "I Want To Hold Your Hand" which (last the last few singles) is a duet/double vocal between John and Paul.
The hosts enter the picture after this musical set with a bit of (supposed) humour and then they all get together to sing "Moonlight Bay" with the Beatles wearing barbershop style jackets and straw hats. Family entertainment at it's finest. :)
This particular show would not be broadcast for another three and a half months (it was finally shown on April 18 1964).
As far as audio goes, most of the show can be heard on the Apple 3-LP/2-CD "Anthology 1" which has the two side of the single as well as the "Moonlight Bay" section. The entire show can be found on audio on the CD "Mythology, Vol. 1".
As far as video goes, the DVD of the "Anthology" series has the "Moonlight Bay" section as well but none of the original live tunes.
I've added a link to the show added to "Youtube" posted by "TheBeatlesApple".