Doctor Who and the Beatles
A clip from the 1965 episode 'The Chase' where the Doctor, Ian, Barbara and Vicki watch the Beatles play 'Ticket to Ride' on the Time/Space Visualiser.
The original idea for the Beatles segment was to depict the band performing at a fiftieth-anniversary concert, with the Fab Four dressed up as old men. It appears that the musicians themselves were interested in the proposition, but it was vetoed by their manager, Brian Epstein. Subsequently, it was thought that an appearance by the Beatles on Top Of The Pops might be used instead, but no footage was available as most editions of the programme were destroyed after broadcast. A November 1964 recording of "I Feel Fine" was then considered. In the event, however, footage of the band performing "Ticket To Ride" at Riverside Studios on April 10th was made available to Martin's team.
The Beatles had a guest appearance on Doctor Who in 1965 -- singing "Ticket to Ride." Afterwards, a traveller from the future remarks that she's heard of the Beatles, having visited their memorial in Liverpool, but that she didn't realize that the Beatles also performed "classical music." This is black-and-white Doctor Who comedy gold.
The original recording of that particular Beatles performance has been lost along with a lot of the BBC library which was tragically thrown out in a great video tape purge in the 1970s. That Doctor Who footage is now the only visual record of that performance.