Let's dive in head first here. In early February 1968, the Beatles were in the studio to record some songs for a projected new single. Nothing had been decided about what songs would make the A and B sides, but they were under pressure to record a single as they were about to embark on long trip to India and would not be back in England until summer.
In January they had recorded George's The Inner Light, but like his Only A Northern Song and It's All Too Much - unreleased from the previous year - there was no chance it would be an A side. So on February 3rd, Paul brought in Lady Madonna and the basic recording was done. The next day John's Across The Universe was recorded. Although it is clearly one John's loveliest and most gentle songs, at the time it created a rift, as Paul had brought in some Beatle's groupies off the street to sing harmonies - a move which left John feeling that Paul was undermining the integrity of his work. Many times over the preceding years John and Paul had engaged in a game of one-upsmanship to write the next Beatle's single. What was different this time was John perceived an attempt to degrade his effort. Whether that is true or not we will never know. Regardless, the outcome is that Paul won this current battle.
On February 11, the Beatles entered the studio to record a film to accompany Lady Madonna. But John had meanwhile written a new song - Hey Bulldog and the LM video was actually a film of the fab four performing Mr. Lennon's new rocker - with LM music superimposed over it. Luckily the original version with HB survives. A stinging guitar riff launches one of The Beatles' hardest rockers.
I have no gripe with Lady Madonna being the initial single A side. In fact I consider it to be the most perfect power pop tune ever recorded. The piano boogie, the goofy lyrics, Paul's Elvis voice, amazing harmonies, kazoos, a saxaphone solo, and a very interesting guitar riff (would love to hear it in a more pronounced role) make it one of the enduring classics. In a kind gesture to George, John recommened The Inner Light for the B side, and being George's finest Indian-influenced songs, it deserves its place.
But what of Across The Universe and Hey Bulldog? The former sat on the shelf for over a year, then was given away as an album track for a World Wildlife Fund fundraiser. A transmogrified version appeared a year later on Let It Be, over-produced, slowed down, and expunged of its sweet potency. Meanwhile the latter song was held until being released as filler on the Yellow Submarine soundtrack.
If someone had been minding the farm, a much better result could have been managed. As a follow up single to Lady Madonna, Hey Bulldog b/w Only A Northern Song could have kept the Beatles on the singles charts until June. At which point Across The Universe b/w It's All Too Much could have kept the streak going until Hey Jude appeared in August. Besides keeping fresh Beatles product on the air, it would have prevented the late-period Beatles singles from becoming the nearly all-McCartney-composed affair that transpired. That John did not fight for these two great songs to be released was a clear sign that the Beatles were entering troubling times ahead.