According to Wikipedia, Horton recorded this version for release in the Commonwealth countries. Most of the pronouns and only a few other words are changed, compared to the version released in the US. I have boldfaced the differences below. I found this on Spotify, where it is called "The Battle of New Orleans - special version cut for England." It is from an album called "The Spectacular Johnny Horton," which also has the American version.

THE BATTLE OF NEW ORLEANS (Commonwealth version)
Written by Jimmy Driftwood
As recorded by Johnny Horton.

1. In 1814 we took a little trip
Along with Colonel Packenham up the Mississip'.
We took a little bacon and we took a little beans,
And we met the bloomin' rebels in a town in New Orleans.

CHORUS: We fired our guns and the rebels kept a-comin'.
There wasn't nigh as many as there was a while ago.
We fired once more and they begin to runnin'
On down the Mississippi to the Gulf of Mexico.

2. We looked up the river and we see'd the rebels come,
While we had at least a hunnerd of us beatin' on the drum.
We stepped so high and we made our bugles ring.
They stood beside their cotton bales and didn't say a thing. CHORUS

3. Old Hick'ry said they could take us by surprise
If they didn't fire their muskets 'til they looked us in the eye.
They held their fire 'til they see'd our faces well,
Then they opened up their squirrel guns and really gave us ... well ... CHORUS

BRIDGE: Yeah, they ran through the briars and they ran through the brambles
And they ran through the bushes where a rabbit couldn't go.
Ran so fast that the hounds couldn't catch 'em,
On down the Mississippi to the Gulf of Mexico.

4. They fired their cannon 'til the barrel melted down,
So they grabbed an alligator and they fought another round.
They filled his head with cannon balls and powdered his behind,
And when they touched the powder off the 'gator lost his mind. CHORUS

REPEAT BRIDGE