There are (or were back when BT was a monopoly) several levels of ex-directory. IIRC, they were...
Not in the printed directory, but available from directory enquiries. Not in the printed directory nor available from directory enquiries, but can be operator connected. Not in the printed directory nor available from directory enquiries nor operator connection. Not even available to most BT staff.
One of these last two is called NQR "No Quoted Record". The others all have names too such as XD, but I can't recall what they all are now -- this was a long time ago.
You could choose one of the first 3. The last one was only available to the likes of senior politicians, royalty, security lines, etc, and also to a colleague back at the time who got someone in BT to mark his line as such as a demo when they were explaining it to us. This caused him both some amusement and some grief years later when he found it was still marked, as there were other implications too, e.g. Faults dept had to pass him on to a special dept to deal, as they couldn't see any info about the line on their computers.