Fair Dealing for reseach or private study
"Fair dealing" with a literary, dramatic, musical or artistic work, for the purposes of research or private study does not infringe any copyright in these works or the typographical arrangement of published editions of these works.
Fair dealing has been interpreted by the courts on a number of occasions by looking at the economic impact on the copyright owner of the use; where the economic impact is not significant, the use may count as fair dealing. So, it is probably within the scope of the above fair dealing exception to make single photocopies of short extracts of a copyright work for the purposes of research or private study. It may be possible to ask a librarian to copy a short extract from a copyright work for you if you are not able to do it for yourself in a library.
The research and private study exception is a little different for databases protected by copyright. In this case, fair dealing is only possible for research for a non-commercial purpose or private study. However, not all copying from a database will infringe copyright in the database - this will depend on whether a substantial part of the database is being copied - but the contents of a database may also be protected by copyright, and extracts of the contents can, of course, only be copied if this use falls within the scope of the general "fair dealing" exception.