How long have rats been running up drainpipes,so to speak ? 'He was off like a rat up a drainpipe' (he got away very fast ). I only noticed the expression when a Welsh friend used it, but it sounds more London than Swansea.Is it a widely-used expression ?
In Monty Python's 'Life of Brian', someone is referred to as moving "like a rat out of an aqueduct", which is, I suspect, just a variant of the probably earlier 'drainpipe' phrase. The film appeared 30 years ago, so your version may have preceded that, in answer to your 'How long...?' query.
In the 50's when I was little we used to have rats in the rear walled garden. If you chased them they did indeed run up the drainpipes to get away from you. I can remember my dad packing the top of a drainpipe and setting a fire at the bottom to kill one.....
I should have added, in possible support of your London provenance, that the words actually sounded like "la' a ra' ah' an aqueduct"...with glottal stops galore. Mind you, that may just have been a script requirement rather than an indication of source!