You can find links to a large number of British and foreign newspapers in the Newspapers section on Databases A-Z
Individual titles include: the Guardian (1821-2003) /Observer (1791-2003), the Irish Times (1859-2007) and the Scotsman (1817-1950) - which are all available via Proquest Historical Newspapers; the Times Digital Archive and the Times Literary Supplement Centenary Archive.
There are also fully searchable newspaper collections, such as ProQuest Historical Newspapers, and the 17th and 18th Century Burney Collection Newspapers and the 19th Century British Library Newspapers collections, and databases such as Nexis UK and Factiva, which include links to newspaper articles.
For help wth using some of these resources see the following guides:
17th-18th Century Burney Collection online help
19th Century British Newspapers online help
(These resources are only accessible from a computer connected to the University of Oxford network, or by logging on remotely using your SSO username and password)
Proquest Historical Newspapers online guide
Nexis UK and its search tips
(N.B. If you are not connected to the Oxford network you will need to login with your Oxford Single Sign On username and password to gain full access to the above online resources)
For information on hard copy newspaper holdings in the Bodleian Libraries, see this presentation on 17th-21st Century Newspapers or visit the Main Enquiry Desk in the Old Bodleian Lower Reading Room.
You can search for a title via SOLO and then use the drop-down boxes to locate a specific issue
You can also access printed copies at the British Library Newspaper Reading Room at St. Pancras in London, for details see: https://www.bl.uk/collection-guides/british-newspaper-archive
The newspapers section of Databases A-Z contains a large number of newspapers covering a wide geographic area and time period. Some of the key resources you may find useful include:
17th & 18th Century British Newspaper Collections
1800 - 1900 British Newspaper Collection
This collection provides access to thousands of items selected from the John Johnson Collection of Printed Ephemera, offering unique insights into the changing nature of everyday life in Britain in the eighteenth, nineteenth and early twentieth centuries. Categories include Nineteenth-Century Entertainment; the Booktrade; Popular Prints; Crimes, Murders and Executions; and Advertising.
http://johnjohnson.chadwyck.co.uk
For a demo of how to use the John Johnson Collection please go to: http://johnjohnson.chadwyck.co.uk/help
This collection spans the period from the mid-1800s to the present day and covers:
This archive is freely available on the web at: http://www.advertisingarchives.co.uk/
You will need to register to view larger images and save picture searches.
A Quick Start guide is available at: http://www.advertisingarchives.co.uk/en/pages/quick-start.html