Right so this is exactly the kind of thing that gets me out of bed at 2am with my recorder. Have you checked whether the sound has any kind of rhythm or pulse to it? The reason I ask is that a few years back I had something similar in Hampshire, low droning noise that just sat outside my bedroom window for about four nights running. Turned out when I ran the recording through Audacity there was this really faint secondary frequency underneath the main hum that you couldn't hear with the naked ear.
Could be infrasound, could be something geological, could be something a lot more interesting. Upload the file if you can, even just chuck it on Google Drive and share the link. A few of us on here have decent audio analysis setups and we can have a proper look at it. What direction does it seem to come from, roughly? And does it stop at any particular time or just fade out?
