Advice

What advice would your give to a year 12 who hasn't been very proactive in their studies or work experience/extra-curriculas but wants to get into UCL/QMUL/LSE etc

that's very true
im currently predicted BBA
B in both econ and maths and A in sociology, im looking at pursuing a degree in either actuarial science or accounting and finance

firstly why are you not proactive, is it that you don't care? I assume not perhaps its an organisational issue.
before I talk about how to solve this issue, as its very easy and wonderful you have/ or at least trying to do so.
https://www.lse.ac.uk/study-at-lse/undergraduate/degree-programmes-2024/bsc-actuarial-science
based on lse you are 2 grades what they want, granted with a contextual you'll close the gap. however I assume you'll be wanting an a star and two as since I haven't checked for econ but do remember that the typical offer is that ( had a friend who did econ at lse.) point being you need to do some work now to make your yr 13 easier.
before you start anything, make a routine, have a rest day like sunday. where you plan out your week. then once you have planned out, there may be an issue,such as an unexpected test, or homework. do them first and reschedule. basically, start using your time wisely. you only have one year till your exams are you ready, gcse's which you've done are nothing like a level. even if you get below a grade that could mean you are no longer on the course. so naturally the stakes are higher.
it would be ideal to have done work experience in yr 11 summer as lots of time, and less to worry about. plan for your easter some work experience if you can get some in time and if not plan for this summer in yr 12. that will solve work experience issue.
for extra circulars follow your passion, maybe you like debating or sport continue that. do some super circulars while you are at it such as reading books on economics, clichue but Rich Dad Poor Dad is a book that could be on your list. just slowly make changes one by one, such as now starting to plan your work. ( I didn't like planning but the sooner you get started the better). also if you do have that much time take a leadership role because why not?
point being lse and other unis are too difficult to get into, but its your mindet and how you behave compared to everyone else. some people may start working seriously later, some may slack off. you don't need to do too much work. do just the right amount for you and hopefully that will help with your academics.
sure some of this is generic advice but may it help you somewhat.