First post, so I have a lot to learn...
No Sgt Pepper for a start, John would most likely have a breakdown, failing marriage to Cynthia (I think at this time), dead mother, dead collaborator/chief band-mate and friend. He'd probably sink into drugs deeper than he did in real life perhaps end up like Brian Jones.
I doubt the Beatles would carry on without Paul at this point as in my opinion Paul was instrumental in them entering the Pepper phase of their career.
George wouldn't go to India with the other Beatles, and would likely not become a Hindu so many of his songs would be radically different.
Ringo would probably go off and become a country-style singer, there are mentions of 'Don't Pass Me By' earlier on so maybe that would come about but in a more primitive form.
John would likely come back in 1969 after hearing of Janov and his primal scream therapy. He wouldn't have learned Travis picking off Donovan, so his guitar style would be different for some songs and no Yoko (Paul caused them to meet each other).
So John's comeback in '70 wouldn't be called Plastic Ono Band, and he'd probably have quite a few songs written such as half of 'A Day in the Life', 'Being for the Benefit of Mr Kite', 'Good Morning, Good Morning', 'I Am the Walrus', 'Strawberry Fields Forever', 'Hey Bulldog', 'Come Together', 'I Want You', etc
I'd see his 1970 album called 'Strawberry Fields Forever' featuring a cover depicting the gates of Strawberry Fields with John standing between the columns. Perhaps Side One being devoted to growing up much like the original plan before Pepper was an album about their childhood, and Side Two devoted to the pain of adulthood, songs like Mother and Isolation, all about loss and suffering.
http://www1.salvationarmy.org.uk/images/uki.www_uki_ihc/strawberry field gates.jpg
George would likely become a guitarist akin to Clapton for a bit, going from band to band. George had a big admiration for the Band and Bob Dylan, so I can see something happening there. Perhaps, George goes touring with Bob or eventually participates in the Basement Tapes, maybe even a George/Bob collaboration album. Until that point, I can envisage George throwing himself into work with Eric offering him a job joining a four-piece Cream with Eric Clapton who'd be recording their debut at the time.
Who'd take the place of the Beatles in culture in Britain, I'd like to see it be the Kinks. In 1968, the Kinks would release one of their best albums 'Village Green Preservation Society', which was overshadowed by the White Album, after all it was released the same week. Maybe, the Kinks wouldn't be overshadowed and gain their first big no. 1 album buoyed by the success of the famous song 'Days', the Kinks would then spread across the Atlantic with the 'God Save the Kinks' movement. Their quintessentially British attitude would be taken in Britain as 'one of their own' whilst the Americans love a bit of Britain.
Other repercussions would be in the Beach Boys, legend has it that when Brian Wilson was showed 'She's Leaving Home' by McCartney in the SMiLE sessions, he began to go mad, thinking they were stealing his ideas. No McCartney and no She's Leaving Home would mean the release of SMiLE possible, and today, it would likely be received as one of the greatest albums of all time. But who'd fill the Pepper spot, the Kinks' Village Green or maybe their follow up Arthur, or SMiLE?
Sorry if there are any inaccuracies but I'm a newbie.
