Depending on your course choices, you may find all the law report series cited in your readinglists and footnotes it textbooks are supplied online via the two generalist databases below:
There are some specialist law reports which are only available online via other databases:
Sources of transcripts of court decisions available to all with access to the internet
Judicial Committee of the Privy Council
The JCPC "is the highest court of appeal for many current and former Commonwealth countries, as well as the United Kingdom’s overseas territories, crown dependencies, and military sovereign base areas. It also hears very occasional appeals from a number of ancient and ecclesiastical courts. These include the Church Commissioners, the Arches Court of Canterbury, the Chancery Court of York, prize courts and the Court of Admiralty of the Cinque Ports."
Practice Direction (Citation of Authorities)  1 WLR 780 (Lord Woolf CJ). In English courts law reports are to be cited in preference to transcripts, and the Law Reports published by the ICLR (AC, Ch, Fam, QB/KB) used in preferrence over other general (eg All ER) or specialist (eg FSR) report series where the same case as been reported in the ICLR.
From 2016 a volume 4 was added to the WLR service. The new 4 WLR is only available online. It contains "additional cases which, while not meriting full print publication, add useful knowledge and provide helpful recent examples of the application of settled law, in a form that can be cited as a complete case report."
Holders of an Oxford SSO can access them via LexisLibrary, Westlaw Edge UK and/or ICLR Case Reports