The key to Westlaw access is to link from a Library page so that you pick up Queen's authentication (rather than going directly to the Westlaw homepage).
You can do that e.g. by searching Library Search for 'Westlaw' from the Library homepage and then selecting 'Go to this resource' from Library Search link for Westlaw UK. Alternatively you can access the A-Z Databases list, navigate to W and then Westlaw UK.
This will ensure access both off campus and on campus. If you are off campus (i.e. not on the Queen's network) you will be asked for your normal Queen's id and password.