While setting up their equipment to play, the Quarrymen's sometime tea-chest bass player, Ivan Vaughan, introduced the band to one of his classmates from Liverpool Institute, the 15-year-old Paul McCartney.

This historic occasion was the first time McCartney met John Lennon, a year his senior. McCartney wore a white jacket with silver flecks, and a pair of black drainpipe trousers.

The pair chatted for a few minutes, and McCartney showed Lennon how to tune a guitar - the instruments owned by Lennon and Griffiths were in G banjo tuning. McCartney then sang Eddie Cochran's "Twenty Flight Rock" and Gene Vincent's "Be-Bop-A-Lula", along with a medley of songs by Little Richard.

“I remember coming into the fete and seeing all the sideshows. And also hearing all this great music wafting in from this little Tannoy system. It was John and the band.

I remember I was amazed and thought, 'Oh great', because I was obviously into the music. I remember John singing a song called Come Go With Me. He'd heard it on the radio. He didn't really know the verses, but he knew the chorus. The rest he just made up himself.

I just thought, 'Well, he looks good, he's singing well and he seems like a great lead singer to me.' Of course, he had his glasses off, so he really looked suave. I remember John was good. He was really the only outstanding member, all the rest kind of slipped away.”

- Paul McCartney, 1995 (Record Collector)

Lennon was equally impressed with McCartney, who showed a natural talent for singing songs that the Quarrymen worked hard to accomplish. McCartney also recalled performing on the church hall piano.

“I also knocked around on the backstage piano and that would have been A Whole Lot Of Shakin' by Jerry Lee. That's when I remember John leaning over, contributing a deft right hand in the upper octaves and surprising me with his beery breath. It's not that I was shocked, it's just that I remember this particular detail.”

- Paul McCartney (John Lennon, Philip Norman

The Quarrymen's set, remarkably, was recorded by an audience member, Bob Molyneux, on his portable Grundig reel-to-reel tape recorder. In 1994 Molyneux, then a retired policeman, rediscovered the tape, which contained scratchy recordings of the band performing Lonnie Donegan's "Puttin' On The Style" and Elvis Presley's "Baby, Let's Play House".

The tape was sold on 15 September 1994 at Sotheby's for £78,500. At the time it was the most expensive recording ever sold at auction. The winning bidder was EMI Records, who considered if for release as part of the Anthology project, but chose not to as the sound quality was substandard.

After the Quarrymen's show the group, along with Ivan Vaughan and McCartney, went to a Woolton pub where they lied about their ages to get served.

Later on, Lennon and Pete Shotton discussed the young McCartney, and whether to invite him to join their group. For Lennon it was a dilemma - should he admit a talented member who may pose a challenge to his own superiority within the group, or should he persist without McCartney, retaining his leadership yet likely consigning the group to failure?

They decided McCartney would be an asset, and roughly two weeks later Shotton encountered McCartney cycling through Woolton. Paul mulled over the invitation to join and eventually agreed to join the Quarrymen's ranks.

Let’s finish off with some of the tunes that the Quarrymen and John & Paul for messing around with on that fateful day.

And here are two super rare Quarrymen recordings, from 1958. By now the line –up was John, Paul, George Harrison, Colin Hanton on drums and John "Duff" Lowe, on piano.