Adding extra sparkle to that resume... or no?

ALs I plan on taking:
Mathematics (Core, Further Pure)
Physics
Economics

Course I plan on taking at university level:
Economics

However, as it is, my extra-curricular list is woefully short.
- School Mathematics Team
- Joint School Mathematics Society
To get into Oxbridge/LSE, should I take up more extra-curriculars?

It's more about what you say about the extra-curriculars than the number of them. You need to spend around 70% of your PS on the subject, which only leaves around 1000 characters for extra-curricular stuff. If you have too many it can come across as like a shopping list, as you don't have room to fully explain each one.

You also need to consider the impact of the time spent on anything. You need to meet your offer, which means you need excellent grades in your A Levels. If you need lots of study time to achieve this, you might not have time to spend on other less important things. Remeber it's not just the time taken with the activity, but also the journey there and back, getting ready, washing kit etc.

Sure, but make sure that they tie into your area of interest (economics). I imagine that US universities won't be as stringent with these, but in the UK you're expected to prove how your extracurriculars pump up your interest for a subject, or academic ability. Cambridge uses the term "super-curriculars" instead of "extracurriculars", highlighting how your interests need to build on top of the subject you're applying for, not outside it.

To provide an example, I'm currently studying Law, and only mentioned my debating/MUN interests in my personal statement, as opposed to my guitar skills. This is because debating exposes you to quasi-legal debates, and helps your argumentation and communication skills, both of which are necessary for Law. On the other hand, me playing the guitar does very little to enhance my academic profile other than proving commitment to a certain activity, which I could show in other ways.

I think mathematics is probably a decent starter (they require A as a baseline I believe) to show commitment and also interest in applications of mathematics? Then I could also join the joint-school economic society in my city in addition to being an intern/shadowing over summer if that works?