Hi Peter
They can refuse to provide the information. However you can get preliminary discovery in the Federal Court to determine whether you have a cause of action against them. They would be foolish to resist such an application.
Has the information you provided them since become publicly available other than by their breach?
What you will want to weigh up is what remedy you could obtain even if you could prove the unauthorised use of the confidential information. Provided the information hasn't otherwise become public you should be able to get a declaration and injunction preventing them from using the information, moving forward, for however long the agreement provided the information was to remain confidential.
None of this comes cheap, however. The cost of filing Federal Court pre-discovery application would be in the order of $10K plus ongoing costs of the proceedings which will easily double the initial costs, but probably much more.
Having said that, after filing the application the other side should capitulate at that point and hand over the documents to prevent further costs being incurred that they would be ultimately responsible for. That has been my experience in any case.
Happy to advise you in respect of your particular circumstances if you want to get in touch.
Len