In terms of laws that will limit the privilege of the House to send for records and papers, there's no explicit law that diminishes or limits this power.
As the privilege is constitutional in nature, the parliamentary privilege is not amended or modified by implication or indirectly. There needs to be an explicit provision in the law that will override the privilege.
There are some privileges—the privilege of freedom of speech, for example—that create some limitations, but those limitations are very explicit. There are none in relation to this power.
We know of some circumstances in which the law of parliamentary privilege does not apply. For example, the House cannot compel the production of Senate documents and the Senate cannot compel the production of House documents, but these are exceptions that arise from the law of parliamentary privilege and not from any acts of Parliament.