Council Tax bills may be possible to fake. I received a paper one yesterday for an unknown name, someone had registered online that they were moving to my address which cancelled my own account, I guess they could have asked for a copy of the bill to be emailed to them.
I’d imagine that all of this stuff is extremely easy to fake if you’re willing to take a small risk of getting in a lot of trouble. Nobody is really “verifying” council tax bills or utility bills because there is no procedure for doing so.