This is clearly not the original version, but it doesn't sway my point. This song, in all renditions, begins in one key in the verses and changes key twice during the chorus, ascending by two whole tones and then one whole tone. In this Eurythmics version, the verses are in G major, the first two lines of the chorus are in B major, and the last two lines of the chorus are in D major. The song ends in G major.
It's almost like the excitement level ramps up as the singer talks about getting married. Notably, there are no minor chords in this song, which makes it feel artificially happy, which to me makes sense because this song is whimsical.
But what I find most fascinating is the transitions. We jump from G major straight to B major: the G descends to F# while the D ascends to D# and the B stays put. Then we jump right into D major: the F# remains as the D# descends to D and the B descends to A. Then we have a V-I to G again to restart the cycle.
Illustrated:
G B D/
F# B D#/
F# A D
While it has no bearing on anything, I'd like to point out that all three keys share the chord Esus2 (E F# B.)