Albert was Albert Kendall, who married Paul's aunt Milly (becoming "Uncle Albert") and provided inspiration for a portion of this song suite. Albert had a habit of getting drunk and reading from The Bible; the only time he read from the Bible was when he was drinking.
McCartney combined pieces of various unfinished songs to create this; in the later years of The Beatles, they did this a lot as a way to put unfinished songs to good use. As a result, "Uncle Albert - Admiral Halsey" contains 12 different sections over the course of its 4:50 running time. This jumble of musical textures, comic character voices, sound effects and changing tempos turned off a lot of listeners, but many others thought it was brilliant. The song wasn't released as a single in the UK, but in America it became McCartney's first #1 hit as a solo artist.
Linda McCartney is credited as a co-writer on this song with Paul. She sang background and contributed some of the vocal ideas, but how much she actually wrote on the song is questionable. Paul had some incentive to credit her as a songwriter: under a deal he signed with The Beatles, songs he wrote until 1973 were owned by Northern Songs publishing and Maclen Music. By splitting the credits with his wife, he could keep half the royalties in the family. The publishers brought a lawsuit against Paul for this practice, which was settled out of court.
This song won the Grammy Award for Best Arrangement Accompanying Vocalists in 1971.
The flugelhorn solo that leads into the "Hands across the water" section was played by American bebop trumpeter Marvin Stamm.