Mate, this is exactly the kind of thing that keeps me up at night even when nothing happens - genuinely can't imagine how wired you must be right now.
A few things I'd want to know if I were you:
How long did it hover? Duration is massive for ruling stuff out, Any sound at all? Drones have that distinctive whine, helicopters are obvious - silence is where it gets interesting, Did it move off suddenly or just... fade?
I'm mostly an EVP person myself so visual sightings aren't really my wheelhouse, but I've got my Zoom H5 running in the garden most nights and I always forget that pairing audio capture with a visual encounter would be absolute gold. Kicking myself reading this that I've never thought to set up a camera alongside it.
Hampshire fields are surprisingly active if the local reports on here are anything to go by - there's something a bit odd about the chalk downlands at night and I can't fully explain why I think that, I just do.
Definitely worth posting the rough location (even just the general area) and checking if anyone else in the thread spotted something the same night. Corroborating witnesses from miles apart is when these things go from ". Probably explainable". To genuinely unexplained.
What did your gut tell you it was?