You find pre-arranged sets of tunes in Scottish published collections from the middle of the 19th century onwards. It was less common before that but I've seen references to the same practice from the 18th century. So the origins of the practice aren't because of recording, though I think JK is right that the marketing of recordings may have encouraged it.

The longest and most complicated medley I can think is the Maltese dance "il-Maltija", which is far too long for a 78. Some Victorian quadrilles are nearly as long. You also get medleying in Viennese waltzes - "The Blue Danube" is six tunes put together.

A very long dance with no change of tune does have a trance-like effect that a medley can't achieve. The electronic dance music scene is simply reflecting a tradition older than most documented British folkdance when they do the same thing.