I don't think many papers have digitised their archives in this way (it's a huge job). Most of what you'll find online just covers the period since they set up their websites. This site should take you to newspaper sites generally:
The Times digital archive is available free of charge, but only at public libraries (this is not currently available for home use). The Guardian/Observer facility (mentioned by vehelpfulguy above) can be accessed at home, but there is a charge. You can buy subscriptions by day, month, year, etc.