The Memex they're taking about (Angleton is a character from The Laundry Files) is an electromechanical filing system for microfiche.

It was never built IRL, so it's difficult to get into the nitty-gritty of security details, but I'm pretty sure that Van Eck phreaking would get you at most the index positions of the documents being accessed, and you'd need optical surveillance to discover their content.