Do you by chance have a Windows computer with iCloud Control Panel installed on it?
What I've noticed is if you have iCloud Control Panel installed on Windows 8+ while Windows is syncing your bookmarks with your Microsoft account, it causes this problem.
The reason I've come up with is that iCloud creates bookmarks on Windows, which Windows will in turn upload them to your Microsoft account, which changes them in a way that iCloud doesn't like it so it pushes the changes out to your phone via iCloud, which then changes it to a format it likes, and sends that back to your Windows computer via iCloud and again starts the vicious cycle of battery drain.
Remove iCloud from your computer or turn Safari sync off on your phone and see if this fixes your battery drain issue. If you have more than one battery powered Apple device, you may want to do the same on those.
Alternatively if you use Mac more than Windows and only have 1 Windows computer, you can just turn the bookmarks/favorites sync off on your Windows computer to your Microsoft account.
This suggestion seems to have solved my problem. I had a 6s experiencing massive battery drain, clearly because of a processes running in the background. I had tried absolutely everything, long sessions with support, restoring to a spare handset, every 'battery saving tip' I could find online. Nothing worked and I was getting 20% battery loss per hour. With a clean install my phone was fine, as soon as I signed into iCloud and the problem returned. The one significant test is if your 'Battery Usage Time' is close to your Battery Standby Time', it means something is thrashing away in the background all the time.
Anyway, I run two Windows 10 machines with iCloud Control Panel - I found this post, signed out of iCloud on both, signed into iCloud on my phone and, two days on, all is looking fine.
I've no idea what caused the problem, the vicious synchronization cycle between Windows and iOS 'mildocjr' mentions seems plausible. All I know is that I can live without iCloud Control Panel on my Windows machines more than i can live without iCloud on my iPhone! Thanks for the tip.
