Ha ha, ok, I was completely wrong. Will try answering those again without jumping to conclusions!
Turns out there is a tiny hole in this pipe (hopefully visible from the yellow mark, with the stream spraying out between the blue lines):
Running from the brew boiler to here (pipe highlighted in blue):
With the case off it was immediately obvious as much to the delight of my kids whose chairs I was using to prop the machine up, I got hit in the face by a tiny stream of water about 5 secs after turning the machine on.
Any tips on replacing that pipe?