The Times Digital Archive provides a facsimile of the newspaper from 1785-1985 and is one of the resources available via the Birkbeck eLibrary.
It is possible to search by keyword on topics as diverse as the abolition of slavery, the establishment of the UN, the debate surrounding Britain's entry into the Common Market and the miners' strikes of the 1980s.
Also available within the archive are the Times Law Reports, simply enter the party names to find a specific case, or try searching by keyword to find reports on a particular subject. (Use Advanced Search to limit your search to the Law section.)
I should add that I find this resource rather addictive, so not one to look at if you've an exam or essay deadline looming!