It is worth consulting the BL's catalogue which has a dedicated newspapers search (via Advanced Search).
This is useful of course for checking the BL's excellent newspaper collections. However, even if you don’t want to go to the BL, the catalogue is useful for finding out which newspapers exist.
For example if you want to know what local papers covered an area you can search by place name. Once you know the name of the newspapers for the particular region you can then search for them in SOLO.
The British Library has released of a metadata list of all British, Irish, British Overseas Territories and Crown Dependencies newspapers held by the British Library. This is now available on the British Library’s open access Research Repository as a public domain dataset.
The metadata includes information on the date range, the place of publication, variant (and successive) titles and editions, as well as whether or not a title has been digitised.
How to get this list? Just go to British and Irish Newspapers: A title-level list of British, Irish, British Overseas Territories and Crown Dependencies newspapers held by the British Library. and select how you want to download it (spreadsheet, zip file).