And? Then what happened?
In the 1988 black (or chocolate-brown, if you prefer) comedy Consuming Passions, Farris, after a vagrant’s dead body he intended to feed into the chocolate vat turns out to be alive (and Irish, I suppose, though the accent isn’t that obvious to American ears – all he says is that he “has a pair of good shoes waiting” for him at an intended destination), and accidentally goes into the chocolate anyway, he (obviously losing it) begins his address to a gathering with “I met an Irishman on the way here . . .” as though that were the start of a standard, formulaic ethnic joke of a type as universally known in the UK as “Knock-knock” is in the U.S. . . . And I think I might have seen or heard the phrase elsewhere . . . but, how is it usually completed? And where did it come from?
“Oh really?”
“No, O’Riley”
I just heard that in something very recently though I now I forget what that was.
Nobody knows? 
Wikipedia’s brief “Irish jokes” page offers no insight.
I recall a lot of material from Larry Wilde’s The Official Jewish/Irish Joke Book from the early 1970s (back when Polish jokes were actually trendy), but those are all American jokes and there is nothing of the “I met an Irishman . . .” form. Presumably it never crossed the Atlantic. (I am indebted to that book for introducing me to the oxymoronic “Irishism,” such as “Faith, 'tis a fine thing to be alone, especially when your sweetheart is with you!” or “The Protestants live in the North and the Catholics in the South and they’re at each other’s throats as often as not. If only we were heathen so we could all live together like good Christians!”)