Hey MAROINEAAKKI,
Well LSE enjoys a stronger global reputation than the other schools you have mentioned, additionally its is quite popular in the UK as well. Both the MiM & the MSc in Management and Strategy are great program for someone who wants to break into consulting, but maybe the choice depends on what are your goals.
As IamGMG has said, a one year program is appropriate for you if you have a prior idea about the industry & are totally focused towards getting into consulting.
The two common career paths taken by Management & Strategy graduates is in management consulting and finance, with the top recruiters in consulting being McKinsey, Deloitte, PwC, Oliver Wyman. So this degree seems like a good choice.
The two year MiM program on the other hand will not only strengthen your management concepts but also provide you with a specialization. As you have mentioned that you have no prior knowledge about business topics, so I believe a two-year program can be beneficial for you.
Additionally it'll allow you to build you business fundamentals and maybe explore more about the different industries.
For example when i started my MiM i wanted to go into consulting as well (I have an engineering UG), but as i studied and learnt more about the industry I came to develop a love for marketing, so well it pays off to get to know the business land scape more.
I will suggest you to check out the review of LSE's MiM program here-
https://www.mim-essay.com/lse-mim-review/ also look into the specialzied masters, compare the pros & cons properly and then take a call.