A recommended place to start when carrying out advanced legal research is the law Library Guides. There are guides on finding cases and legislation, finding books and articles, citing and referencing, and practical legal research. The guides contain information, guidance and links on carrying out research and recommendations for which databases to use to find particular resources.
Databases can be found in Databases A-Z, it is possible to filter by law from the drop-down menu to display all law databases. The databases include general databases such as Westlaw and Lexis+ for finding cases, legislation, articles and commentary; and specialist databases on particular topics, such as i-Law (maritime, commercial and insurance) and Kluwer Arbitration.
If your research crosses over into other disciplines such as economics, healthcare or finance, it is worth looking at the Library Guides for other schools. They contain guidance on which databases and resources to use to find information in those subjects.
To find journal articles, a good starting point is Westlaw. It has a legal journals index which goes back to 1986 and contains all UK and English-language European law journals. For foreign law journal articles use the HeinOnline Law Journal Library. It contains articles from across the world and can be filtered by location and country published.
For international law and national law from other jurisdictions use Westlaw International which can be found on the Westlaw homepage, or use the international tab on Lexis+. Both contain legislation, case law and articles from a variety of different jurisdictions.
Outside City University, a very good option for advanced legal research is the Institute of Advanced Legal Studies (IALS). The IALS library has a vast range of legal resources including extensive coverage of international law and other jurisdictions. PhD students and academic staff from any UK university are able to join the library and admission is free. For more information about IALS see their Library Guides.