I was just wondering whether rdiff-backup (which I use locally) could be persuaded to use encryption -- the easiest way would probably be to do the backup onto some kind of encrypted drive, rather than encrypting each individual file (it works over SSH so the end-to-end encryption is already sorted).

TBH the main problem with such services where you're storing encrypted data is the liability issue for the service with whom you're storing it. I'm sure our beloved Government -- or, if not ours, then the US's -- could make a case for prosecuting someone running such a service if it was later found that the encrypted data was something the Government concerned considered "dodgy".