Quote from Richie Unterberger's 'The Unreleased Beatles'
[...]The unpleasantness starts, in fact, with the head-hurting task of trying to get one's head around the mere establishment of when, where and why this stuff was done in the first place. More confusion surrounds the tapes' murky origin than virtually anything else The Beatles recorded. It has been variously theorized that the tapes were recorded at the Art College of Liverpool, where Lennon and Sutcliffe were student at the time; at the Jacaranda club run by their first manager of sorts, Allan Williams; somewhere in Hamburg; or the apartments of John Lennon or Stuart Sutcliffe (who joined the band on bass in early 1960). Estimates for the dates of recording have varied between late 1959 and late 1960. Paul McCartney told Peter Hodgson, who sold him a tape with some of the material in 1995, that it was made in the bathroom of his home (which might at least partially explain the mounds of reverb) during a school vacation in April 1960.
That remains the best guess of date and location, though here's the first place in this volume to note that the Beatles' own memories of such details can't be taken as gospel, not when McCartney was mixing up the order of Rubber Soul and Revolver in a 1999 Mojo magazine interview, to give one example. It's pretty certain that the musicians on these crudities are Lennon, McCartney, Harrison and Sutcliffe. Despite the presence of occasional erratic percussive beats, there's no real drummer involved; according, again, to McCartney, that's Paul's younger brother Mike, who never was an official member of the band. If you were listening to the Beatles for the first time on these tapes, you might assume that Paul was the undisputed leader, as it's his singing that's heard by far the most often.
[...]
Unbelievably, there are few performances here that are even up to the level of the demo disc of 'That'll Be The Day' they'd cut almost two years or so earlier. As Peter Doggett wryly observed in Record Collector, the 1960 tapes, in contrast, "suggested the Beatles were running their carreer in reverse...they offered no hint that by the end of the years their creators would be unquestionably the best rock 'n' roll band on Merseyside."
There's a lot more information about these tapes, but this is the most relevant part about dating the tapes.
