A couple of my mother's carers have been parking up in the theatre car park in the small hours to listen to "the whistler". Some nights he goes on and on and on. There's nothing to be seen and it's impossible to say just where the sound is coming from; if they step out of the car it stops immediately. They've recorded him- and he sounds like a bloke whistling as he goes about his work- something very few people do these days because of the Walkman and its successors. It's not a mechanical sound. It goes up and down; it's tuneful, but the tune is unidentifiable. The guy's improvising.
A bird? What, at three o'clock in the morning? I don't think so.
C says they've made enquiries and someone told them the area used to have a milkman who whistled on his early morning rounds. My best guess would be that he's left an imprint.