Keith Gregson in his Corvan - A Victorian Entertainer And His Songs devotes a section to the tale when discussing Ned Corvan's song on this - essentially the version that appeared in Allan's Tyneside Songster and given by Conrad Bladey in the Lyr Add thread in the links. He discusses the truth of the legend (and I speak as a native of Middlesbrough with no axe to grind) as below:

"It is one of the few Corvan songs to have survived in balladsheet form and the Public Library at Hartlepool of 'Who Hung The Monkey'...

'Who Hung The Monkey' proved to be the original of a song which appeared in Allan's Tyneside Songs as 'The Fisherman Hung The Monkey, O'. The main difference between the two versions is that the earlier one, written down from Corvan's act, was slightly cruder than the version which appeared in Allan's...<examples excised - MCP>...

The later version of the song is well-known in Hartlepool but neither Allan's Tyneside Songs nor Hartlepudlians have given Corvan enough credit for creating the myth <myth excised - MCP>...

Few people have ever maintained that this story was true and the tendency has been to trace its origins to the new town of West Hartlepool where, in the 1840's the inhabitants were only too ready to scoff at hte past deeds of those from the old town. This being the case, Corvan's contribution was merely to take a myth already in existence and turn it into a song to please local audiences.

Robert Wood <local historian - MCP> researched thoroughly into the origins of the myth of the Monkey and found very little that could link the story as it is told today with the Hartlepools of the 1840's. Strange tales of monkeys did exist in the area at the time but nothing that would link in with the idea of the Napoleonic spy. Only after Corvan's appearances in Hartlepool is there strong evidence for the development of the Monkey story and it is possibly on Tyneside, thirty miles to the north, that a clue to the myth's origin can be found...

Corvan grew up and performed in an area where 'monkey stories' were already in existence and, what is more important, where they existed in the form of songs...<2 examples excised - The Sandhill Monkey 1827 and The Baboon - based on a monkey dressed as a soldier brought by some Cossacks to the Tyne during the Napoleonic wars, this latter song referring both to Bonaparte's uncle and a hairy French spy>...

Was it merely coincidence that the Monkey in Corvan's song should turn up as both 'Napoleon's uncky' and the 'hairy French spy'? Certainly The Baboon is a song which...Corvan must have known...If the origin of the Hartlepool Monkey story does lie here, and Corvan simply used it to mock the fishermen in his audiencethen he may well have played a larger role in the development of the myth than was previously thought."

Mick