My wife and I worked in fields related to copyright and libraries respectively for many years, so I can tell you this:
Under the copyright law, you may copy part of a book for research purposes. "Part" is often defined as one, maybe two chapters, or maybe 20 per cent, but is not specified in the law.
"Research purposes" includes any private individual researching for his own private purposes. You do not have to be a university professor or journalist or any other kind of professional researcher to make copies for research. You do not need to prove or disclose the nature of your private research.
The copyright law applies to all "literary works" as posted already, which means all printed matter, not just Shakespeare or Irvine Welsh etc.
But libraries can make their own rules, based on whatever whims please them. And increasingly poorly trained staff (most are not actual librarians these days) often get confused or can't be bothered sorting out what's what and just decide to not allow copying at all. Which makes you wonder why they would have a copy machine at a library.
You should take the issue up with the head librarian. They are falling down on the job if they are failing to allow patrons to pursue private research at their library. If they are in doubt, suggest they check with their professional association, CILIP (Chartered Institute of Library and Information Professionals.)