When searching for legislation, you can use one of several options: Westlaw or Legislation.gov.uk.
Which resource you use largely depends on what additional material you are looking for. Legislation.gov.uk will provide the most basic information, i.e. the text of the legislation and amendments, whereas because Westlaw and Lexis contain much wider legal material, these databases will also cross-reference with relevant journal articles and cases.
So if you want to research a particular piece of legislation - for example, cases that relate to it or thoughts of legal experts regarding it, you are better off using Westlaw or Lexis. If you just want to see or download the text of the legislation, then you can easily find this via Legislation.gov.uk.
Westlaw is probably the best place to start searching for legislation if you are not sure what you are looking for, or if you want to explore further or related material in connection with a particular Act or section of an Act. Because the Westlaw database also contains journal articles, law reports, expert insights and more, when browsing legislation you can also access this related material, making it easier to do research into a particular piece of legislation.
For further guidance on using Westlaw to find and research legislation, please explore the Westlaw user guide (linked here) or watch the video below.
The best place to search for EU cases is the main European Union portal, EUR-Lex. This is the official site for all EU law, containing EU case law and references to national case law relating to EU law.
Documents in EUR-Lex are available in English, as well as all the languages of the member states of the EU. However, the coverage in a particular language will only date from when that country joined the EU; material is not translated and added retroactively. So, for example, Croatia joined in 2013, so only documents and material added since 2013 will be available in Croatian (Hrvatski).
There is no one source for international law, so you may have to scout around depending on what country's law you are interested in.
Bear in mind, that very few countries make all of their case law freely available online, not even the UK. You can usually access UK judgements online via the Courts and Tribunals Judiciary website, but the detailed law reports are usually only available via paying for them, and this is often a similar issue across the world. In addition, where judgements are available online, they are unlikely to be in English, unless you are looking for cases from a country where English is one of or the official language.
A good place to start looking for international case law is WorldLII. You can select the country you are interested in, and it will provide relevant links, where they exist, to case law available for that country, as well as legislation, parliaments, government structure and departments, etc.