It is always worth trying to track down the paper which may have first printed the news item. As today, bad news in particular (an unfortunate accident for example) travelled well, and could appear in a number of different papers (sometimes quoting the source). Your best option is to search for alternative local publications assuming copies survive for dates you need.
For the UK you could consider the
Online British Library Integrated Catalogue which lists local newspapers titles.
You might also consider purchasing a copy of Local Newspapers 1750-1920.
Compiled by Jeremy Gibson, Brett Langston, and Brenda W. Smith. ISBN 1-86006-157-5It should be stressed however, that even searching the British Library integrated catalogue and buying the guide to local newspapers by Jeremy Gibson
will not guarantee that you will be able to locate the issue of the newspaper you need. Not all copies of newspapers have survived. This may not be apparent until you search the microfilm or original copies at the British Library at Colindale and other repositories.