What broke up the Beatles was Paul's public announcement on April 10th, 1970, that the Beatles would never work together again, and the subsequent lawsuit he filed against the other three on December 31, 1970.
Until then, no matter what they said privately to each other, all their public statements conveyed the message that the partnership was to continue indefinitely.
In the fall of 1969, after "Abbey Road" was released, John told Melody Maker that "after 'Get Back' is released in January, we'll probably . . . do another one." In February of 1970, he told Rolling Stone, "We still might make Beatles product . . . but we need more room--The Beatles are just too limited., that's where the trouble is." He told the New Musical Express, "It just depends on how much we all want to record together." He said that trying to accommodate everyone's songs on one album was the main problem.
Ringo told NME in March of 1970, "Everything's fine. I've got things to do and George has got things to do and Paul has his solo album and John has his peace thing. We can't do everything at once." George said, in the same article, "Say we've got unity through diversity, because that's what it is . . . we had to find ourselves, individually, one day."
When John Eastman (Paul's brother-in-law and attorney) announced on April 7th that the release of Paul's solo album, "McCartney," was coming out and it meant, in essence, the end of The Beatles, Apple spent three days denying it before it reluctantly released, on Paul's demand, the "self-interview" (subsequently was included in UK copies of "McCartney") that made the split official.
On that day (April 10), Apple also released a statement on behalf of the Beatles that read, "The world is still spinning and so are we and so are you. When the spinning stops--that'll be the time to worry. Not before. The Beatles are alive and well and the beat goes on. The beat goes on."
Even after the April 10th announcement, the remaining three Beatles were still publicly stating that the Beatles, as an entity, still existed and this was a temporary hiatus. A few weeks after Paul's statement,
Ringo told a reporter, "I just feel it in my bones that we'll probably all be recording together again before very long." George said, "There is every prospect" that the Beatles eventually would work together again. "Everyone this year is trying to do his individual album, but after that, I am ready to go back to work together again." In early summer, George, while working on "All Things Must Pass", again said he'd expect the Beatles to be working together, possibly by the end of the year.
the info was taken from the site The Beatles – Breakup