I theory you need a licence to watch iPlayer live. If you are watching programmes after they were aired then you don't - in theory. Of course it's difficult for them to prove it in the first place. Even if you let them into your premises, they aren't going to be able to tell what you watched and when without checking your Internet files and, unless they have a search warrant, you can refuse to let them touch your computer.
It's not actually a crime to own a TV set without a licence and if you let them in and they saw a TV set, you'd only be breaking the law if you switched the set on when they asked you to.
The mistake people make is in thinking that because these people seem official, you have to do what they tell you. You don't.
Years ago - when I worked for the Post Office, the TV licence people used to contract postal workers to do their investigations. I knew a few people who worked for them and what they could or could not do.
"Goodness is about what you do. Not what you pray to."