"Music with rocks in" - British English?

I've been reading a multitude of Terry Pratchet books lately, and been exposed to some British terminology that doesn't generally make it over to the states.

The book Soul Music refers to rock music as "Music With Rocks In". That bothered me at first. As an American, I expect there to be a pronoun at the end ("Music with rocks in it").

Is this merely a quirk of Pratchet's writing, or is it common to drop the pronoun at the end of a phrase like this? Might a British purchase order a "burger with cheese in"?

It's not an uncommon construction: it had never occurred to me that it was particularly British, but maybe it is. It is generally colloquial.

The British National Corpus has some examples (there may be many more, but there's no easy thing to search on):

Yeah put on that er you know the little jumper with buttons on not the yellow one but the blue one.

Do they like not like it with nuts in or like that? [I guess there's a pause and correction after the first "like"]

There's also the very common colloquial intensifier "with knobs on":

In consequence, fascism was to emerge in Britain in the 1920s as a supposed imitation of Mussolini's example in Italy, although in reality it was little more than ‘Conservatism with knobs on’, in Arnold Leese's graphic definition of the British fascists.

I've a feeling that "with a hat on" is the same construction, but I guess it could be argued that "on" there is a kind of adverb rather than a preposition.

It's a joke. Both the slightly odd grammar and the literal phrasing (rock music doesn't really refer to stones and pebbles) are supposed to be a bit "off" for humour purposes. I love Terry's books and have them all, but they are so deep in puns I can't imagine what it must be like to read them in my second language. For example Veterinari is supposed to remind you of Medici, only slightly less so, just as a vet is not quite a doctor.