Answer: When the Post Office/Royal Mail/Parcel Force has a package to deliver that is 'Signature Required'.
A package was sent to me from Germany on Dec. 17. The Tracking Number used on the German Post Office website confirms that it was accepted by Great Britain on 27 Dec. Ok, it's the holiday season. The UK system can tell me nothing about its whereabouts. Apparently, the Tracking Number will only be of use when (if) it is signed for. It cannot be used for tracking the package, despite being a Tracking Number.
I called Parcel Force, and they said that it was not one of theirs, probably because it was to small (correct, it is, it's a record player cartridge). Royal Mail said that it was probably one of theirs, but they couldn't track it, and recommended that I go to my local Post Office and ask there. I did, and they said that there was no way that they could track it, to tell me where it was, and they could not tell me whom to ask. 'Wait a few more days'. And then what?
What a way to start the year!