Newspaper content may be out of copyright, or in copyright:
In case of newspapers fair dealing applies:
Anybody can copy an 'insubstantial part'. This is not defined in law, but almost certainly precludes anything materially useful by itself. A single copy, in any format, of a 'substantial part' may be made under fair dealing for private study or for research for a non-commercial purpose, and the generally accepted upper limits of what constitutes a substantial amount that can be copied within fair dealing are as follows:
Any more than this is probably not fair dealing. Nor is it fair dealing to copy, say, one article from a book or journal on one occasion and another article from the same book or journal on another occasion. Note also that introductory and similar matter are not excluded, but should be treated as chapters or articles.
A library may make and supply to you a copy, in any format, of part of a published work within the same limits. The librarian will ask you to complete a copyright declaration, which limits your use of the copy to private study or non-commercial research.
Copyright in a newspaper article typically expires 70 years from the date of the author's death. The copyright in anonymous works expires 70 years from the date of publication, but you should be aware that lack of a byline (signature) on an article doesn't necessarily mean it is anonymous.
For more information see government guidance and information from the National Archives.
Oxford University has a license agreement with the Newspaper Licensing Agency (now called NLA Media Access) but it is complex - the University's Press and Information Office should be consulted about any proposed use.