According to the Incoporated Council of Law Reporting (ICLR), "A law report is a record of a judicial decision on a point of law which sets a precedent." In the UK, they are typically published accounts of cases heard in the High Court and Appeal Court (in England & Wales), and in the Supreme Court (formerly the House of Lords). Not all cases are reported, and "a decision is only reportable if it lays down a new principle of law" (ICLR). For more information on the definition of a law report, read ICLR's page at: https://www.iclr.co.uk/knowledge/glossary/law-report/.
There are many series of law reports, and the reports are either published in printed form, or available via online services, such as LexisLibrary. Some of the more authoritative reports, include The Law Reports and The Weekly Law Reports, both published by the Incorporated Council of Law Reporting for England & Wales (ICLR), and The All England Law Reports (published by LexisNexis Butterworths). Some are of a specialized nature, only covering certain areas of law; examples are: Criminal Appeals Reports and Industrial Law Reports.
Most reported cases and some judgment transcripts (or 'official transcripts') can be located in either LexisLibrary or WestLaw UK legal databases. Another good online source is British & Irish Legal Information Institute (BAILII).
With Law it is of paramount importance that you keep up to date with the sources you use and that the law you are referring to, both legislation and cases, is 'good law'. Citators and alerting services can help with this:
The Appeal Court practice direction of 2012 clarifies the practice and procedure governing the citation of legal authorities and applies throughout England & Wales, including the Crown Court, county courts and magistrates courts. Where a law report is available, particularly if the case has been reported in one of the 'official series'; e.g. The Law Reports published by the ICLR, it must be cited and referred to in preference to any other. (See Practice Direction (Citation of Authorities)  1 WLR 780)
You can refer to tools which provide you with the list of law reports for particular cases in order of authority. Tools to look at include:
Westlaw Case Analysis documents
LexisLibrary's Case Overview database
Individual cases are often arranged collectively in Law Reports.
To locate a case you need to be able to understand the citation.
E.g. Fisher v Bell  3 W.L.R. 919
The different parts of the Citation are explained below:
Law reports can either be found online or in the Law Library. Check the title in the Library Catalogue for the best source.