The tune is an old Irish Air. Star of the County down is only one of the many songs that has used it. In my opinion its better played as the original slow air. I don't this that the speeded up versions like "Star" does it justice. I believe that the original Air was called "My love Nell" ... maybe someone has put words to it since with the same name.
I do a version of "The Lancashire Lads" with this tune that I got off Mike Harding.