G'day,
There's a song called The Bold Fusilier which uses the Cowan version of the Matilda tune. It has been suggested that Paterson simply rewrote this song. Here is what Richard Magoffin says about it:-

There is an English song which pretends to come from the time of the Duke of Marlborough, "The Bold (or Gay) Fusilier", but it is really a parody of "Waltzing Matilda" from the Boer war, which was attended by the fusiliers, by Banjo Paterson, and many other Australians who sang our song. (Also, although irrelevant here, by Marlborough's descendant Sir Winston Churchill - A of A).

There is no record anywhere of the existence of this song prior to 1900 by way of any manuscript.

The British Museum wrote in 1968 that they had never found any trace of the song. The British Folk Song and Dance Society had received many requests but, likewise, found no record.

The Mayor of Rochester and the editor of the Fusilier's magazine were challenged some years ago to present pre-Matilda evidence for their song. They were not able to do so, while insisting that hearsay evidence in England was sufficient. English folklore authority, Vaughan Williams, considered that the earlier existence of the song was very doubtful because its language was not appropriate to the early eighteenth century period it pretended to represent.

There are two versions of this in the DT:-
MARCHING THROUGH ROCHESTER and
COME BE A SOLDIER FOR MARLBORO AND ME
These are attributed to Peter Coe. Both are significantly different from the version on Peter and Chris Coe's "Open The Door And Let Us In" album whose sleeve notes say of "The Gay Fusilier": A recruiting song set at the turn of the 18th century. Peter found the first verse and directions for the tune (said to be originally English) in a magazine, but after searching unsuccessfully for the rest of the song, he wrote the additional verses himself.

Cheers,
Alan