|F M Lehman|
Bb | Bb | Bb | F7 | F7 | F7 | F7 | Bb
I doubt whether many musicians today know that Royal Telephone was written in 1919 by Frederick Martin Lehman, an America immigrant from Germany. His piano music is available on the internet.
I noticed that it is really necessary to treat the song as a 32-bar, with 16 as 'Verse' and 16 as 'Chorus'. There were originally five verses (The first beginning 'Central's never busy - always on the line') and the Chorus - repeated after each verse - comprises the 16 bars always beginning with the words 'Telephone to Glory, Oh what joy divine!'
The chords I have printed above match the Chorus (and that is probably why they are followed so rigidly by most traditional jazz bands). However, if you want to play the tune correctly and include a verse or two, you need to use the following VERY slightly different chord sequence for the verses.
Bb | Bb | Eb | Bb | F7 | F7 | F7 | Bb
To see what I mean and to hear a really clear performance of the song, complete with vocal, listen to the version by Burl Ives on YouTube by clicking here. But note that he begins with the Chorus before singing the First Verse.
Footnote: Curiously, if you play Enjoy Yourself, It's Later Than You Think, you may find a remarkable similarity with Royal Telephone, at least in the chord progression.