no way does she not remember that! Did no conversation take place? Have you tried to jog her memory - I paid on X, you came up to me and said... we were in the ...
Was anyone else around? Can you remember what she was wearing? Can you remember anything she said?
And don't accept her going round telling people that! in the first place you're under no obligation anyway! What if you didn't want to, what if you couldn't afford it? She's got no business involving other people. How dare she?!
I have a very unfortunate evil streak
so based on the fact that she has chosen to involve other people and basically badmouth - I would be going on the attack. "I paid the day after she asked and she hadn't got the card. So she took my £20 and now she's claiming I never gave it. I suppose she could have forgotten, but that's £20 extra in her purse, isn't it? I wonder why she can't find it..."
But don't do that
it's not a very attractive trait.
Probably assertive might be the way to go? "I HAVE given you £20. I am not prepared to give you another £20. If you can't find it, or you've spent it, you will have to put it back in yourself. And please don't go around gossiping about me."
How very convenient for her that she has no memory of taking this money from you.