she had not == (British English)?

I asked her for some paper but she had ………….

a)none ([color=green]Answer Key)
b)not
c)no
d)nothing

Hello again,
I remember when I was a kid, my school English books were British not American.
In those books I remember I usually saw these British sentences:
For example:
[color=blue]1. Have you a pen? No, I haven’t. [although in American we say “Do you have a pen? No, I don’t.”]
So, according to this evaluation, can’t we say that in this test option B (not) is correct according to the way British people talk? I mean such as the above blue example written in my school books: ???
Like: Had you a pen? No, I had not. =====> ???
And guidance?

I asked her for some paper but she had ………….

a)none ([color=green]Answer Key)
b)not
c)no
d)nothing

Only (a) is correct, whichever ‘version’ of English you use.

Thank you.