The principal printed reports which include modern English criminal cases are listed below. The usual abbreviation used in citations to each report is given in bold first, as that is what you will see in footnotes and tables of cases.
These citations can be used in subcription databases to find, at least, the transcript of the judgment. If the case was subsequently reported, then the database will alert you to this fact.
International Human Rights & administration of criminal justice
Crim LR is the abbreivation for the Criminal Law Review - in other words, a specialist law journal (which happens to publish useful case notes) not a law report series.
As it is a journal, it is shelved among the journals.
OU members have online access to this journal - but only from 1986 onwards - via Westlaw UK (see link below)