The trick to advanced searching in LexisNexis is the "Search by Content Type" button in the upper right. Clicking this button will reveal a menu of different News, Legal, Company, and People search types within LexisNexis.
The International Legal section has three options: Canadian Cases, Canadian Legislation, and EU, Commonwealth, and Other Nations. British cases are in the EU, Commonwealth, and Other Nations section.
Enter your search terms or case name. Make sure to choose the correct jurisdiction (UK Cases, Combined) in the Source box.
Scroll through the search results until you find the correct case. The case you're searching for will probably be the oldest case in the list, which may put it at the end of the list.
Clicking on the case name will give you the full text. Note that LexisNexis Academic does not include as many features (like Shepardizing or headnotes) for non-US cases.
The search interface for WorldLII is fairly straightfoward--enter your keywords into the search box. When searching for cases, you can limit by jurisdiction in the "Advanced Search."
Because WorldLII draws from multiple sources, you may have duplicate search results. And because the owners of the source documents often move them, some of the links may be broken.
Try the links until you find one that opens a copy of your case.