The title attribute for the most recent xkcd strip has the value "Supercollider? I 'ardly know 'er", with apostrophes in place of the two initial h letters. This is a cultural mistake, a rare thing from Randall Monroe, who is usually pitch perfect.
Randall's use of apostrophes suggests that instances of this old joke must belong to one of the English varieties that "drops aitches". But in fact, many (most?) speakers who generally preserve [h] generally don't have an [h] in unstressed versions of the pronouns he, his, him, her. For me, and I think for most Americans, an initial [h] in the object pronoun of "I hardly know her" (or "I hardly know him") would sound rather fussy and over-articulated. So the joke doesn't have to be delivered in a Cockney accent!
I'll leave it to the commenters to try to determine who invented this joke, or at least when it came into common use. A quick internet search turns up dozens of variants of the first clause, including the topical "Spitzer". It's easy to create new ones, since -er is such a common ending in English (and -or etc. will work as well).
And if you pick a random er-final word, there's a depressingly high chance of finding it involved in an instance of this joke on the web — Randall is not the first (or even the 30th) to apply the pattern to supercollider.
There are fewer examples with him, no doubt partly because words ending in -im or -um etc. are rarer, and partly because people are less likely to make such jokes about men. Some obvious opportunities (like bunkum) haven't yet appeared on the web (compare bunker).
For more on the cultural history of English [h] in general, and [h] in unstressed syllables in particular, see "An hero at the NYT", 2/16/2004; "An hero ain't nothing but a hypercorrection", 2/6/2004; "Hung like a hero", 2/16/2004; "A shibboleth of gentility: [h] from William Shakespeare to Henry Higgins", 3/1/2004.