It is always good to start the research by first checking the indexes. The Law Library is subscribed to the following indexes and they can be accessed electronically through the library catalogue or the eResources @ Osgoode page.
The Law Journal Library in HeinOnline provides access to journals published in the United Kingdom. You can do a browse search or in the "Field Search" limit your search to "United Kingdom" under subject.
Select Sources and filter by country by selecting "United Kingdom". Select "Law Reviews & Journals" which gives you a list of all the journals available in this database.