It was a common enough song in its day, and still turns up from time to time; not infrequently in much-condensed (and sometimes frankly obscene) forms. You can trace it back to a London broadside song of the second half of the 17th century, Room for a Jovial Tinker, in which the hero is only disguised as a Tinker in order to get into the house without attracting suspicion. In later forms the subterfuge is dropped and we get instead a real Tinker and more sex.

Number 863 in the Roud Folk Song Index; examples are listed from most English-speaking countries. For various texts and more background (including links to broadside editions), see thread Duchess and the Sailor.

I don't know how that Donnelly fellow got into a version of it, but all sorts of strange things happen with songs like this.