They can in theory tell what channel you are watching, when you are tuned into a certain frequency the signal the tuner emits is a set distance from that of the signal you are receiving. So if you are watching ITV analogue you are emitting a signal slightly above or below (I can’t actually remember which it is) the ITV signal – proof that something is tuned into ITV.
Of course this is all in theory and in practice they probably do none of this. Showing them that there is no aerial connected and no channels are tuned in normally gets rid of the inspectors.
But you don’t have to let them into your house unless they have a warrant, and they can’t get a warrant without giving a magistrate some evidence that suggests you are watching TV. Despite all their publicity it isn’t all that easy to do, especially if you have a shared aerial.
But what they can do is take you to court, send a summons through the post asking you to turn up in court, where they will ask you under oath if you are using a TV without a licence. You can plea by post, and the vast majority of these get sent back with a guilty plea.
The ability to receive TV, as I said, does not mean you need a licence, you only need a licence if you are receiving broadcasts.