Westlaw or Lexis are the best databases for finding a UK case. You can search by case name, subject or citation in both databases, but they cover different law reports, so you might have to search them both.  If it is a very recent UK case, BAILII is also worth searching.

Westlaw is a good place to start your search for current legislation and historic legislation for the UK, EU and some other jurisdictions. You can search by the name of an act or a subject. It will also tell you if it is still in force or repealed.

Westlaw and Lexis both contain full-text journal articles, so start with one of those. They contain different journals, so it is best to search both for better coverage of a subject area. Scopus is also worth searching, as it covers a range of subject areas, including law.