Gurney's interesting post shows how the lyrics were updated for a later audience, both relating to Arsenal and the Beefeaters verse.

The football references are in the original song which in 2003 Joe copied into this thread from a post by Charles Colyer in 1997 to a thread about Halloween songs:

The sentries think that it's a football
That she carries in
And when they've had a few they shout,
"Is Ars'nal going to win?"
They think it's Alec James
Instead of poor old Anne Boleyn,
With her head tucked underneath her arm.

The mention of Alec James is, I think, a reference to Alex James, a famous Arsenal player of the time. He helped his team win the First Division Championship in 1930-31, 1932-33, 1933-34 and 1934-5 (He was injured during the 1931-32 season and Arsenal were only runners up!) The song was written in 1934 so he was at the height of his fame then. He didn't score so many goals himself, but provided an abundance chances for others (or "assists" as we say these days.)

The Beefeaters verse seems to me to be a later improvement over the original verse:

Sometimes gay King Henry gives a spread
For all his pals and gals, a ghostly crew.
The headsman carves the joint and cuts the bread.
Then in comes Anne Boleyn to "queer" the "do";
She holds her head up with a wild war whoop
And Henry cries, "Don't drop it in the soup!"

LFF