Has there ever been any release (If so, where can I get a download) on the music from London Spy by David Holmes and Keefus Ciancia? I'm really just interested in that one melancholy descending theme that would pop up every now and then.

There's no release for "London Spy," but you can find an excerpt here: https://soundcloud.com/yann-kerjan/london-spy-excerpt-from-soundtrack

Darn, that's what I was afraid of haha. Alright, although I can't get it on the go, this should be good for now, thank you!