I have now completed tables of the full, long titles of public statutes passed by the parliament of the United Kingdom of Great Britain and Ireland, from the Act of Union in 1801 up to 1921, when Ireland was divided and the south achieved independence. They can be found on github. <url> All these tables are public domain, and can be reused for any purpose and in any way one wishes.
I am currently working on generating tables of abbreviated titles of private and local acts for this period, using the annotated lists of local acts and private acts produced by Legislation.gov.uk <url>
This will be quicker than working through the full titles in the volumes of statutes for this period, although at the cost of less detail. (Tables giving full titles will be produced eventually as I work on correcting the OCR of the scanned volumes, but this will take some time.)
Once the private and local tables have been created, I will produce a more convenient package of these lists, easy to download and suitable for searching and text mining.