Thank you both for your answers.
Here's exactly what is says on the form:
The other referee must normally be
the holder of a British citizen passport and either a professional person or over the age of 25
The fields where you write the passport number for both referees have this label:
Current British citizen passport number (if any)
Now, the
if any part tells me that the passport number is indeed not required. However, since it doesn't matter which referee is on the left-hand side and which is on the right-hand side, and the professional referee doesn't have to be a British citizen, the optional passport number may only apply to them.
I suspect that it doesn't matter if the second referee has a passport, however whether that might cause delays - I don't know.