Hi

A certain little girl was hypnotized and taken to the coven. She was taken there by Miss Thorby who hypnotized her.

During the coven her teacher managed to snatch her away and hid her in a room.

When she was "normal" again (she was hypnotized) she said to the teacher:

Thass how they got me here and out of my clothes. You see,
Miss, the very last thing I ever said to Miss Thorby was
that I never would. That was the day she was seeing if the
belt fitted. The minute I see it, I knew how I’d been had;
as bad as if I’d stayed with my gran. I said to her they’d
never get me . . . and the next thing here I was with you,
and they had as good as got me.

I can't figure out what she mean by "I never would"? Maybe I never would allow them to get me?
Yes. That's all the context supports. The only other possibility is 'I never would let them get me out of my clothes.'
By the way, is there a difference between: I would never allow them to get me/to get to me?
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Yes. Would you like to put them into sentences that trouble you?
For example:

They got me AND They got to me.

I didn't want to go somewhere/to do something, but they got me/they got to me.

I would say in both cases it means they "caught" me.
They got me = they caught me

They got to me = they reached my position; they affected my emotions.
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