It opened without speed limits, crash barriers, a central reservation or lighting, at a time when there were fewer than five million licensed cars on UK roads compared with more than 28 million now.
The musical was created by BBC Radio Northamptonshire and features a number of people who have worked, visited and dined at the rest-break location.
Previously called the Blue Boar, people originally made special trips to visit its restaurant and dozens of stars including Dusty Springfield, The Beatles and the Rolling Stones are known to have stopped there.
Mr Mole described the M1 as a "motorway with an iconic past".
"It's a road that's certainly grown in use. People know it and love it, and probably hate it as well," he added.
The road now stretches 193 miles from Brent Cross in north-west London to Garforth near Leeds.
Steven Jukes, from the Society for All British and Irish Road Enthusiasts, said: "Before the M1 there was no real idea of long distance travel. It opened up a way of living we couldn't really have anticipated."
Over the years, Watford Gap services has become an unofficial demarcation point for the perceived north-south divide and a signpost was unveiled on Sunday at the "boundary".
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