TV License

Cornucopia

The OP says that they received the letter after a long period of being Licence free at a new address, so it's possible that the letter was the one they send at the end of the "No Licence Needed" period, and that does kind of ask if a Licence is needed yet.

The problem with the BBC "wanting" to find out if a household is watching without a Licence is that they have no legal power to demand that information or to make threats about whether it is provided or not.   (And they don't really believe anyone, anyway).

Uriziel

Just a note that if you contact them and let them know they have your details which they need to acquire a warrant and enter your home so if they wanted to they could get a court warrant and pay you a visit and you would have no choice but to let them in. They would be able to point at any screen and say that you watch BBC online and then take you to court. This is why people always say to just ignore them completely. Without a name they cannot get a warrant.

Cornucopia

Uriziel said:

Just a note that if you contact them and let them know they have your details which they need to acquire a warrant...   Without a name they cannot get a warrant.

They don't need your name to obtain a warrant, and a TV Licence warrant will typically not have a name on it (just an address). 

What they do need is evidence of evasion, which they can only really get if you give it to them (either verbally or by opening the door to them with evidence on in the background). 

TV Licence warrants are so extremely rare that they aren't really something that anyone who genuinely doesn't need a Licence needs to worry about.