LSE MSc in Economics

Hello everyone,
I'm seriously considering an application to LSE in this program, and I'm a bit confused by what this statement of academic purpose is about. What am I supposed to put there exactly?
Otherwise it's pretty clear to me, I have the grades equivalent of a First Honors and I think my CV should be good as well.
Thank you in advance for your answers!

A statement of academic purpose is essentially an academic cover letter. So you want to discuss your interest in the course, your academic background, and why that means you'll do well on the course. There's lots of info and examples available online.
In terms of your chances, having a first doesn't mean too much in reality. It's more about the content and level of the courses you've covered, than just the grades. It's also about your research experience, rather than commercial experience.

Thank you so much for the guidance!
I did my bachelor thesis on financial bubbles, I was the Editor of the Economics section of a journal too (extracurricular, not professional) and I also passed the CFA L1 (which includes parts on Economics and Quantitative Methods), do you think these would help my application?

Journal stuff is good as it links strongly to experience and interest in academic research. On the CFA, it's not directly related to academic economics, so for it to help your application, you need to make the link explicit. Same applies to any work experience.
Topic of your dissertation doesn't really matter - most people do a dissertation. But it is important to discuss it and what you learn from the process, and how this then relates to your interest in doing a MSc in Economics.
I should've been clearer in my original post, but the reason why getting a first in isolation doesn't mean a tonne is that different unis cover different content at different levels. A first from a top uni is very different to a first from a poorly ranked uni. They want to know that after a few weeks of prep and recap classes, you'll be able to pickup the content from where LSE's undergrad left off. Therefore, the uni you get your first from and the content covered in your course is the crucial bit, not just that your grade.

Thank you again for your clarifications!
Regarding the different uni: I did my a Bachelor in Business Admin from a top 3 French business school, would this count for something in that regard? I studied economics during my first three years, as for maths it was spread out across my entire curriculum, although it was related to financial concepts.

I'm afraid I don't know enough about the contents of French business administration courses to be able to give a strong steer.

I'll dive into more details so you can get a better idea:
Economics side: for the first two years, I studied Macroeconomics, Microeconomics, International Economics and Asian Economics. During my third year I took Business in European Economies as an elective, and for my last year of studies, my position as an Economics Editor took over. When I studied the CFA, Economics were part of the subjects and I reinforced my knowledge in Macro and Microeconomics.
I know about supply and demand, I can quantify the impact of different events on it such as tariffs or supply/demand shocks, I also know about business and economic cycles, fiscal and monetary policies and their different uses, market structures, how to integrate geopolitics into the mix, different curves (Kuznets, Laffer...), etc.
Mathematics side: for the first year I studied Maths Applied to Economics and Finance and Statistics. Otherwise, for the remainder of my studies I used maths for disciplines like Accounting, Finance, Cost and Budgets, and for Strategic Management Control (maths were used for measuring KPIs, which took different forms of mathematical functions). The latter part would be more relevant to the electives I intend to take, Corporate Finance and Finance for Mergers, Buyouts and Corporate Restructurings.
Concepts that I studied that would prove useful for the MSc overall were during the first year (Maths applied to economics and Finance, statistics) and when I studied the CFA: statistics and statistical measures, probability trees and conditional expectations, simulation methods, estimation and inference, hypothesis testing, parametric and non-parametric tests of independence, and simple linear regressions, homoscedasticity/heteroscedasticity, etc.
Regarding the CFA: although I learnt those concepts in the context of measuring a portfolio's return and the performance of financial assets, I think those concepts can be transposed for the Econometrics part of the MSc.

I don't want to discourage anyone in applying for a course they're interested, in so please only see this as advice and not some authoritative statement on the issue, particularly given you've done your undergrad degree abroad. But personally I don't think you have the background for this specific course.
Starting just on the basic requirements, I'm not sure you meet the minimum. For the MSc Economics, LSE ask for a minimum of a First in an economics degree, or an equivalent degree that has a concentration in economics and quantitative subjects. For starters, you don't have an economics degree. But you also don't have a degree with a concentration in economics and a quantitative subject (e.g. economics and statistics, economics and CS, etc). In the UK, a business degree with some economics modules isn't usually considered equivalent to an economics degree.
LSE's department of economics has a FAQs page, which goes into more detail on the required maths backgrounds. This says:
"It is not just a case of having taken some Economics, Maths and Statistics courses; successful entrants will have studied, been examined in, and achieved at least First-class results (at least 70%) in core economics courses that are part of a quantitative-based Economics degree structure, i.e. with standard courses in Intermediate Macroeconomics, Microeconomics and Econometrics which then become the foundation to study - and obtain strong results - in a number of advanced courses."
One option might be to apply to their two-year MSc Economics course, this essentially catches you up with all the advanced maths, stats, and economics required for the MSc Economics then you do the MSc Economics. Another option would be to apply to one of the joint courses like their MSc Economics & Management, which is a halfway-house between economics and business administration. A third option would be to also apply to some of the interesting European MSc Economics courses at places like Bocconi, Mannheim, Bonn, Zurich, Tilburg, Stockholm, Paris School of Economics, Toulouse, CEMFI, Pompeu Fabra/BGSE, Sorbonne, Sciences Po, etc where it would be cheaper and you may have a better understanding of how the economics requirements map on to your undergrad degree.