I lived in UK years ago and had some similar experiences.
First time my wife got ill and called up the dr to make an appointment, she was asked ‘are you public or private?’
My wife asked ‘what difference does it make?’
They told her she had to wait three weeks for her dr appointment if public.
If she was public, she could come in that same day.
Did you mean to write that she could come in the same day if she was private?