Relevant work experience is absolutely not necessary to get in for PPE anywhere; I never did any.
For supercurriculars, the main one would be reading. There are lots of reading lists and suggestions out there on the web, such as the ones linked in the post above me. I would recommend starting with some general introductory works on the subjects, as much as anything just to make sure that you know what philosophy, politics and economics are all about, and that you actually will enjoy studying them. Some books I personally found particularly enjoyable and useful were relevant titles in the Very Short Introductions series, The Accidental Theorist by Paul Krugman, Political Philosophy by Adam Swift, and What Does It All Mean? by Thomas Nagel. From there you could potentially move on to some books in more specific sub-fields that you have a particular interest in - in your personal statement, it’s a good idea to talk about some more detailed areas of interest, which will be more impressive to universities than just reciting the stock general reading list. Overall though, don’t feel like you need to read a ton; certainly at no point should you be reading so much that it’s distracting from your school work.
Other than reading, there’s not really any supercurriculars that are absolutely necessary. If your school or college runs any discussion clubs on politics, philosophy, and economics, it would probably be a good idea to join them, and equally a general debating society might be useful, particularly if you’re planning on applying to Oxford (not sure if you are), as it would help to hone the kind of skills needed for interview.
Overall, my advice would be to do what you enjoy, and explore your passion for PPE. There’s certainly no need to overwhelm yourself with supercurriculars at all. By far the most important thing for making a competitive application is to build and maintain a strong academic record, including good predicted grades.