Maybe the phone is turned away so it doesn't reveal the phone number.
Sweetie, how old are you?
That phone isn't about to reveal any number whatsoever.
If it actually has a dial function, it looks like it is of the old rotary dial switch number.
However, I could well imagine that it is a House-call-model,, the call was made and connected by the information desk/room (switch board) at BuckHouse and transferred to the Queen, once BJ was holding the line.
Reminds me of the grandson of friends who found one of those old ones in the attic and wondered how on earth one could write a SMS with it....