The original theme tune from Thomas and Friends is a frequent subject of sampling, remixing and mashups. The comic posing of its jaunty Englishness against, say, Biggie Smalls belies the underlying tune's mix of complex melodies, ragtime, carnie music, and a simple, pounding beat. It is also, as Charles Cornell (previously at BB) points out, unironically really good.
I have an unpublished short story with a scene where the protagonist starts monologuing about this theme the way Patrick Bateman launches insanely into magazine-style reviews of Phil Collins, Whitney Houston, etc. Cornell elaborates on the strange dissonances and unexpected key changes in it: as well as being quite the little banger, it is a subtly weird piece of music. "We ended in a different place to where we started and we don't even notice the transition happening."
Why it works so well as rapper mashup material isn't addressed. The general consensus seems to be that it's just the simple rythym + humor + meme-luck. But it interesting to read how just far back inspiration and appropriation flowed from the music of black Americans to that of the white Britons whose world Thomas evokes. This theme doesn't wander far from the shared elements, then slaps a big fat beat on top.
Also, I wonder if it was mastered with "space for vocals" that were never actually written or put in, which means that cutting and pasting random vocal tracks into it "just works" without making the results muddy or hard to follow.