I always thought (the ancient bloodsport of) cock fighting was more British than Egyptian but heigh-ho.
Then again, it may not refer to bloodsports at all, nudge nudge.
It sounds like Ive Got A Big Bouncing Baby......and I've been googling it and googling it with no luck under that search term and Elvis......Until I put in the next line of the song.....and then I came up donalds with the answer. I really did think it might have been a professional Elvis impersonator that recorded it given that I had no luck....
I like to know the origins of the audiophonic artworks we have to swallow in our jobs....
"Row, row, row your boat, Jesse down the stream"
and although it's not a lyric, she also thought it was:
"Our Father, who art in Heaven,
Harold be thy name...." BRILLIANT