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The words "hose" and "pipe" were both around long before the 1800s so I maintain this "hosepipe" contraction makes no sense.
"Old English hosa, of Germanic origin; related to Dutch hoos ‘stocking, water hose’ and German Hosen ‘trousers’. Originally singular, the term denoted a covering for the leg, sometimes including the foot but sometimes reaching only to the ankle."
https://en.oxforddictionaries.com/definition/hoseOld English pīpe ‘musical tube’, pīpian ‘play a pipe’, of Germanic origin; related to Dutch pijp and German Pfeife, based on Latin pipare ‘to peep, chirp’, reinforced in Middle English by Old French piper ‘to chirp, squeak’.
https://en.oxforddictionaries.com/definition/pipe
I literally just took an Oxford dictionary off the shelf and looked it up. Hosepipe is a word that has been used since the 1800s.
At a guess id suggest that hose refers to the use or action of the pipe e.g hosing something down.