' I do feel that if I pointed out that her behaviour was upsetting me it would mortify her '
No, it wouldn't. And she's relying on this belief of yours to continue taking the piss. It doesn't matter how long you've known her, she's ripping the piss and she knows it. I mean, who the hell does this? We're quite poor/low income. I have friends who are very much the opposite. I've been invited to stay in their homes. I would never in a million years think it was acceptable to rummage round in their personal belongings, much less demand to take them. Because 99% of people know this is unacceptable. Duh.
'I prefer the option of always saying no until she stops.'
And then she'll probably go and steal it.
You need to give your head a wobble.
Start suggesting meeting elsewhere or at hers and you'll bring lunch.
If she demands to go to yours, you text back, 'Actually, I'm very uneasy with your rummaging round in my belongings and asking to take things.'
She's taking the piss and she knows it, just as she also knows you'll put up with it.