Though not any telco bill, it has to be a landline. Otherwise you could spin up a mobile contract and it would be easy. If you're a single person company/consultant they'll accept a personal bank statement (having just gone through this runaround myself).
That's even more absurd. What if I don't have a landline, or somebody else in my household is paying for it?
It seems to be for offices where you'd have a lease agreement. But even my accountant's letter was refused as not proof enough. I believe you can have HMRC send something, but they're not exactly quick and Wise wanted something more urgently. The strange thing is they didn't ask until months after the account was set up and had already approved proof of incorporation for the registered address.