I was reading the 2nd Beatles Monthly Book (released in September 1963), and it contained an interesting account of how the Beatles got started, including John's recollection of meeting Paul.
“There was a friend of mine called Ivan who lived at the back of my house and he went to the same school as Paul McCartney— The Liverpool Institute High School. It was through Ivan that I first met Paul. Seems that he knew Paul was always dickering around in music and thought that he would be a good lad to have in the group. So one day when we were playing at Woolton he browght him along. We can both remember it quite well. We've even pot the date down. It was June 15th, 1955. The Quarrymen were playing on a raised platform and there was a good crowd because it was a warm sunny day.” (John Lennon)
There are a few things in this account that stand out to me.
John says they met on June 15th, 1955, something we now know isn't correct. The commonly accepted date is July 6th, 1957, at the Woolton Fete. The mistake makes me wonder whether John and Paul simply misremembered the date in 1963, or whether there may have been an earlier meeting that later became mixed together with the famous Woolton Fete story.
The way that John tells about Ivan and Paul coming to the Woolton Fete really backs up some people's claim that Paul had the intent of meeting John at the Fete, or at least that was Ivan's intent, taken that he "thought that he [Paul] would be a good lad to have in the group" and ended up bringing him along to the Woolton because of that reason.