The references date from 1987. This database is now available on the QMW CD-ROM network. It's worth noting that apart from its detailed financial news, the FT provides good general news coverage, so is well worth using for non-financial matters. This is a weekly and not strictly a newspaper, but it can provide a useful source of news stories, so is worth mentioning here. We have from 1991 onwards on the CD-ROM network.
Many newspapers have sites on the world wide web.
They vary in the amount of news which they include from their current issues, but most of them include a limited archive which you can search. The University of London Library at Senate House has a good range of titles. Their aim is to provide historic rather than current coverage and they recommend that readers use academic or public libraries for the last 6 months issues. Readers must provide some form of identification in order to use the library. All their holdings are closed access, so newspapers have to be ordered and you should expect to wait up to an hour for delivery.