Success and failure. The child proof locks worked at holding the top of the bin on, but Tully now knows how to open the lid of the rubbish bin - so it just takes a little longer for her to raid it.
So now to work out what to do about the lid. I was just re-reading the thread and I might try some long velcro on the lid.
And then yes, final attempt will be to buy a wire crate and find somewhere to put it!