AS-Level Further Maths

If its not required by any of those Unis, or they don't give a different grade offer plus this AS, then don't bother - its far more important that you get 3 good grades for your main A levels.

The only course that demonstrates some sort of preference to further maths is LSE, and they also believe that economics and business together aren't great. LSE is also my firm choice so I'm stuck between whether it's worth it or not 🥲

Email LSE and ask - but if they are already saying they do not like Econ and BS together, given the competition at LSE, then its possible that you may not get an offer anyway, regardless of any extra AS.
Look at Bath - top Business School and the placements system is probably the best in the UK - Accounting and Finance BSc (Hons) with work placement (bath.ac.uk)

That is quite unfortunate, I'll contact them now. I do believe that students with preferred subjects tend to apply for Finance or Economics which may be a slight opening for me.
Regarding Bath, I was considering it but I'd say I'm set on going to a London based university within commuting distance.

i'm shocked your school allowed you to take BS and Econ - we forbid it precisely because unis don't like it.

Yeah, if I had known prior, I wouldn't have picked it 😭 I've just got to suffer the consequences now ahah