The Beatles Complete on Ukulele project, spearheaded by Roger Greenawalt, aimed to offer up the entire Beatles collection for free. The main caveat: there had to be a ukulele in the music. For the first few years (there are currently in excess of 180 songs in the collection), you could download each and every song in the collection. Not so any more. I haven’t been able to find out the reason for the change: the collection is still available for listening online (http://beatlescompleteonukulele.com and/or http://thebeatlescompleteonukulele.com), but they are now charging to download the songs.
The Beatles included Her Majesty on Abbey Road. As with all the other downloadable copies of these songs, the downloadable ukulele version includes informative inline notes – both about the ukulele version and about the original. For this song, these notes claim that “… the song was originally placed between Mean Mr Mustard and Polyethelene Pam… “ but McCartney asked to have it removed and destroyed. However, EMI policy was that no Beatles recordings should be destroyed and the song eventually ended up as the close to the album (in spite of the song “The End”, which should have been the end of the album.) I assume "her majesty" is Queen Elizabeth?
This version, by Jon Albrink, includes additional lyrics and it sure sounds like he is having a good time. He does the guitar and vocals (http://www.jonalbrink.com/) while John Benthal plays the uke in this 2011 recording. Depending on your browser, the linked file may well show you the "liner notes" I reference above.