While it is unlikely that a natural eidetic currently serves in parliament, memory is something that can be trained and improved.
So you take a willing MP, teach them about mnemonics, memory palaces, chunking, and list-ordering narratives, and you could likely smuggle out a few dozen pages every week.
I've had two students in six years who could perfectly reproduce the information on a textbook page after one look at it, even if they had no understanding of the material.