Can I apply to cambridge/lse?

I don't see why not. Rememberrandom extracurriculars aren't of great relevance for Cambridge (and probably LSE) - UK unis tend to be less interested in generic ECs and more interested in specifically relevant things you've done like wider reading in your subject area. Work experience isn't required or expected for non-professional courses like healthcare oriented courses.
Note if you plan to drop a subject for year 13 I would strongly advise against continuing business studies and economics together with just one other subject for LSE as they state this is considered a narrow range of subjects and would be less competitive. As part of 4 subjects it's fine (although equally you don't get "bonus points" for doing a 4th so I probably would suggest considering dropping one).

I'm an international student and in grade 11 (yr12). I wanna apply for econ at cambridge,lse and other unis like ucl.My gcse equivalents I got mix of 7/8/9s and idh much options for work experience where I live. I tried for internships but didn't meet age criteria as most are for above 18yrs. My academics have been slacking but I'm getting back to it and I've a shot at getting A* in all my subjects. And idh further maths in my school (my subjects are econ,maths,history,business). I've started with reading for supercurriculars. Will I have a chance with stacking up on reading and writing good essays? I'm also the founder and Co-lead for my school's econ club and I'm working on starting a newsletter.

You absolutely do not need any internships for any course at any uni - they are looking solely at your academic interests.
LSE does not like the combination of Business and Econ (I’m pretty sure most unis don’t) so I’d think about dropping or swapping Business for something else.
It’s a shame that your school doesn’t offer FM but people still get in without it.
Work hard towards getting all A*s predicted, do a bunch of essay competitions and find areas of econ that interest you to write about in your statement to make it as good as possible, sounds like you’re already doing some stuff which is great.
Best of luck and if you have any questions about LSE in particular I’m happy to answer them.

Thanks for replying! Yea I saw the uni websites too. Idh the option to drop the subjects but for my predicteds i'll be using maths,econ,history. It's just that I've seen people this year saying they've done all sorts of work experience and other stuff and still being doubtful so it's made me kinda question if I'm just getting my hopes up for no reason esp when Idh the option to.

Thanks! Idh the option to drop a subject but for my predicteds I'll be giving maths,econ,history. For essay comps is it still valuable if I don't win but have a key takeaway I can show? And supercurriculars can u give book recs or other sources, I'm not rlly sure from where to start. I've heard aligning it with the uni book recs is good but then I won't understand without knowing the basics ryt. And do certifications add value (I can only do audit). For tmua dyk what sources I can use (I've heard abt r2drew2). Should I do math olympiads? And just any tips or stuff I should know.

Essay comps are absolutely still valuable if you don't win because you still have to do all the research and plan the essay so you will be able to write about the topic and the things you found interesting about it in your ps too.
As for book recs i mean look at the LSE/Cambridge website I'm sure they recommend books there. For development economics which a lot of people find interesting I'd recommend Poor Economics by Abhijit Banerjee, but honestly just ask chatgpt to recommend you some stuff I mean it's super easy to start with something. You do not have to read the book cover to cover, just make sure you read chapters you find interesting because you will need to be able ot write about it convincingly and if you get called to interview by cambridge they could possibly ask you about it.
They do not care about certifications at all whatever it is. Do get whatever work experience/certifications you want by all means as they may be useful for applying to internships and stuff but just know that for the personal statement they are entirely irrelevant/very minimally relevant.
I did not do the TMUA so can't help with that unfortunately. Maths olympiads would be fine to do but more econ specific supercurriculars are much more important, writing about maths olympiad in the statement would only come if you literally didn't have anything else to write about or you linked it to something in econometrics or something idk.

Alright, thanks sm! Can ik where you're studying and what course?

I'm doing PPE at LSE

How intense is the workload? i.e. How many essays per week? What is your typical day like?
Did you live in halls in Year 1 or commute?

Workload is not bad at all. This year I only have one full day, as in I have lectures and classes (with breaks in between) from morning till evening. Rest of the week I am home apart from going in for like one class on a few days, sometimes I go to campus to meet friends but I mean this so far this year I've been grinding internships very hard so not done much else haha.
You will have problem sets for econ/stats/maths modules, which take 2 ish hours I would say if you want to complete them properly, but you can do them quicker too - I have 2 of them this year. My other two modules require very little work week on week, which is super nice. Essay modules obviously take more work but I don't really have any at the moment.
I lived in halls year 1, which I would highly recommend - I live in London so I commuted last year, commute this year and will do so next year too. Commuting is very decent (I suppose it depends how much you like home and how long your commute is), I mean when I start working I'm going to be commuting as well so may as well get used to it now.
Overall the course is much less intense than at Oxford, I would imagine, there are crunch points and some hard modules but that's to be expected.
The people around you are also going to be less academic (than Oxford, it is still LSE haha) and more career (finance, consulting etc.) oriented, which initially I thought I would dislike, but I now really appreciate, as I realised there is no way I want to go into academia haha. If do you find when you come here that it is something you would be interested in, the research here is obviously world leading and there are many opportunities that way, you'll still find likeminded people.
I am very biased but I couldn't recommend LSE more, I am aware some people have different experiences but just being in London is a massive advantage and overall I have absolutely no regrets. Super international student population and I have friends from all over the world.
Also I'm not graduating this year haha, which is great, honestly all UK uni degrees should be 4 years I don't understand why they're 3. It just means you can ease in more gradually and it doesn't slip away from you as quickly. You can always swap to Phil/econ if you find you don't want to do the 4 years.

I'm an international student and in grade 11 (yr12). I wanna apply for econ at cambridge,lse and other unis like ucl.My gcse equivalents I got mix of 7/8/9s and idh much options for work experience where I live. I tried for internships but didn't meet age criteria as most are for above 18yrs. My academics have been slacking but I'm getting back to it and I've a shot at getting A* in all my subjects. And idh further maths in my school (my subjects are econ,maths,history,business). I've started with reading for supercurriculars. Will I have a chance with stacking up on reading and writing good essays? I'm also the founder and Co-lead for my school's econ club and I'm working on starting a newsletter.